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All Textbook Solutions for Elementary Algebra

Simplify: (a) y64 (b) z53 .Simplify: (a) p85 (b) q136 .Simplify: (a) 813 (b) 644 .Simplify: (a) 6253 (b) 7294 .Simplify: (a) 54p103 (b) 64q104 .Simplify: (a) 128m113 (b) 162n74 .Simplify: (a) 1083 (b) 484 .Simplify: (a) 6253 (b) 3244 .Simplify: (a) x7x34 (b) y 17y54 .Simplify: (a) m 13m73 (b) n 12n25 .Simplify: (a) 532323 (b) 486m 1143m54 .Simplify: (a) 192333 (b) 324n742n34 .Simplify: (a) 108c 10d63 (b) 80x 10y54 .Simplify: (a) 40r3s3 (b) 162m 14n 124 .Simplify: (a) 3x5+3x5 (b) 39393 .Simplify: (a) 10y4+10y4 (b) 53263326 .Simplify: (a) 1923813 (b) 324+5124 .Simplify: (a) 10832503 (b) 645+4865 .Simplify: (a) 32y53108y83 (b) 243r114+768r104 .Simplify: (a) 40z73135z43 (b) 80s134+1280s64 .In the following exercises, simplify. 442. (a) 2163 (b) 2564 (c) 325In the following exercises, simplify. 443. (a) 273 (b) 164 (c) 2435In the following exercises, simplify. 444. (a) 5123 (b) 814 (c) 15In the following exercises, simplify. 445. (a) 1253 (b) 12964 (c) 10245In the following exercises, simplify. 446. (a) 83 (b) 814 (c) 325In the following exercises, simplify. 447. (a) 643 (b) 164 (c) 2435In the following exercises, simplify. 448. (a) 1253 (b) 12964 (c) 10245In the following exercises, simplify. 449. (a) 5123 (b) 814 (c) 15In the following exercises, simplify. 450. (a) u55 (b) v88In the following exercises, simplify. 451. (a) a33 (b) b1212In the following exercises, simplify. 452. (a) y44 (b) m77In the following exercises, simplify. 453. (a) k88 (b) p66In the following exercises, simplify. 454. (a) x93 (b) y124In the following exercises, simplify. 455. (a) a105 (b) b273In the following exercises, simplify. 456. (a) m84 (b) n205In the following exercises, simplify. 457. (a) r126 (b) s303In the following exercises, simplify. 458. (a) 16x84 (b) 64y126In the following exercises, simplify. 459. (a) 8c93 (b) 125d153In the following exercises, simplify. 460. (a) 216a63 (b) 32b205In the following exercises, simplify. 461. (a) 128r147 (b) 81s244In the following exercises, simplify. 462. (a) r53 (b) s104In the following exercises, simplify. 463. (a) u75 (b) v116In the following exercises, simplify. 464. (a) m54 (b) n108In the following exercises, simplify. 465. (a) p85 (b) q83In the following exercises, simplify. 466. (a) 324 (b) 645In the following exercises, simplify. 467. (a) 6253 (b) 1286In the following exercises, simplify. 468. (a) 645 (b) 2563In the following exercises, simplify. 469. (a) 31254 (b) 813In the following exercises, simplify. 470. (a) 108x53 (b) 48y64In the following exercises, simplify. 471. (a) 96a75 (b) 375b43In the following exercises, simplify. 472. (a) 405m104 (b) 160n85In the following exercises, simplify. 473. (a) 512p53 (b) 324q74In the following exercises, simplify. 474. (a) 8643 (b) 2564In the following exercises, simplify. 475. (a) 4865 (b) 646In the following exercises, simplify. 476. (a) 325 (b) 18In the following exercises, simplify. 477. (a) 83 (b) 164In the following exercises, simplify. 478. (a) p 11p23 (b) q 17q 134In the following exercises, simplify. 479. (a) d 12d75 (b) m 12m48In the following exercises, simplify. 480. (a) u 21u 115 (b) v 30v 126In the following exercises, simplify. 481. (a) r 14r53 (b) c 21c94In the following exercises, simplify. 482. (a) 64424 (b) 128x852x25In the following exercises, simplify. 483. (a) 625353 (b) 80m745m4In the following exercises, simplify. 484. (a) 105023 (b) 486y92y34In the following exercises, simplify. 485. (a) 16263 (b) 160r 105r34In the following exercises, simplify. 486. (a) 54a8b33 (b) 64c5d24In the following exercises, simplify. 487. (a) 96r 11s35 (b) 128u7v36In the following exercises, simplify. 488. (a) 81s8t33 (b) 64p 15q 124In the following exercises, simplify. 489. (a) 625u 10v33 (b) 729c 21d84In the following exercises, simplify. 490. (a) 8p7+8p7 (b) 3253253In the following exercises, simplify. 491. (a) 15q3+15q3 (b) 22746274In the following exercises, simplify. 492. (a) 39x5+79x5 (b) 83q723q7In the following exercises, simplify. 493. (a) 234y12+194y12 (b) 315z10175z10In the following exercises, simplify. 494. (a) 8131923 (b) 5124324In the following exercises, simplify. 495. (a) 2503543 (b) 243418754In the following exercises, simplify. 496. (a) 1283+2503 (b) 7295+965In the following exercises, simplify. 497. (a) 2434+12504 (b) 20003+543In the following exercises, simplify. 498. (a) 64a103216a123 (b) 486u74+768u34In the following exercises, simplify. 499. (a) 80b53270b33 (b) 160v1041280v34In the following exercises, simplify. 500. 164In the following exercises, simplify. 501. 646In the following exercises, simplify. 502. a33In the following exercises, simplify. 503. b1212In the following exercises, simplify. 504. 8c93In the following exercises, simplify. 505. 125d153In the following exercises, simplify. 506. r53In the following exercises, simplify. 507. s104In the following exercises, simplify. 508. 108x53In the following exercises, simplify. 509. 48y64In the following exercises, simplify. 510. 4865In the following exercises, simplify. 511. 646In the following exercises, simplify. 512. 64424In the following exercises, simplify. 513. 128x852x25In the following exercises, simplify. 514. 96r 11s35In the following exercises, simplify. 515. 128u7v36In the following exercises, simplify. 516. 8131923In the following exercises, simplify. 517. 5124324In the following exercises, simplify. 518. 64a103216a123In the following exercises, simplify. 519. 486u74+768u34Population growth The expression 10xn models the growth of a mold population after n generations. There were 10 spores at the start, and each had x offspring. So 10xn is the number of offspring at the fifth generation. At the fifth generation there were 10,240 offspring. Simplify the expression 10,240105 to determine the number of offspring of each spore.Spread of a virus The expression 3xn models the spread of a virus after n cycles. There were three people originally infected with the virus, and each of them infected x people. So 3x4 is the number of people infected on the fourth cycle. At the fourth cycle 1875 people were infected. Simplify the expression 187534 to determine the number of people each person infected.Explain how you know that x105=x2 .Explain why 644 is not a real number but 643 is.Write as a radical expression: (a) t12 (b) m13 (c) r14 .Write as a radical expression: (a) b12 (b) z13 (c) p14 .Write with a rational exponent: (a) s (b) x3 (c) b4 .Write with a rational exponent: (a) v (b) p3 (c) p4 .Write with a rational exponent: (a) 10m (b) 3n5 (c) 36y4 .Write with a rational exponent: (a) 73k (b) 5j4 (c) 82a3 .Simplify: (a) 3612 (b) 813 (c) 1614 .Simplify: (a) 10012 (b) 2713 (c) 8114 .Simplify: (a) (125)13 (b) 12513 (c) (125)13 .Simplify: (a) (32)15 (b) 3215 (c) (32)15 .Simplify: (a) (64)12 (b) 6412 (c) (64)12 .Simplify: (a) (256)14 (b) 25614 (c) (256)14 .Write with a rational exponent: (a) x5 (b) z34 (c) y25 .Write with a rational exponent: (a) a25 (b) b73 (c) m54 .Simplify: (a) 432 (b) 2723 (c) 62534 .Simplify: (a) 853 (b) 8132 (c) 1634 .Simplify: (a) 853 (b) 8132 (c) 1634 .Simplify: (a) 432 (b) 2723 (c) 62534 .Simplify: (a) 1632 (b) 1632 (c) (16)32 .Simplify: (a) 8132 (b) 8132 (c) (81)32 .Simplify: (a) 323343 (b) y13y83 (c) m14m34 .Simplify: (a) 535575 (b) z18z78 (c) n27n57 .Simplify: (a) (p 10)15 (b) (q8)34 (c) (x6)43 .Simplify: (a) (r6)53 (b) (s 12)34 (c) (m9)29 .Simplify: (a) u55u14 (b) v35v25 (c) x23x53 .Simplify: (a) c 125c25 (b) m54m94 (c) d15d65 .Simplify: (a) (32x 1 3 )35 (b) (64y 2 3 )13 .Simplify: (a) (16m 1 3 )32 (b) (81n 2 5 )32 .Simplify: (a) m23m13m53 (b) n16nn 116 .Simplify: (a) u45u25u 135 (b) v12vv72 .In the following exercises, write as a radical expression. 524. (a) x12 (b) z13 (c) z14In the following exercises, write as a radical expression. 525. (a) r12 (b) s13 (c) t14In the following exercises, write as a radical expression. 526. (a) u15 (b) v19 (c) w120In the following exercises, write as a radical expression. 527. (a) g17 (b) h15 (c) j125In the following exercises, write with a rational exponent. 528. (a) x7 (b) y9 (c) f5In the following exercises, write with a rational exponent. 529. (a) r8 (b) s10 (c) t4In the following exercises, write with a rational exponent. 530. (a) a3 (b) b12 (c) cIn the following exercises, write with a rational exponent. 531. (a) u5 (b) v (c) w16In the following exercises, write with a rational exponent. 532. (a) 7c7 (b) 12d7 (c) 35f4In the following exercises, write with a rational exponent. 533. (a) 5x4 (b) 9y8 (c) 73z5In the following exercises, write with a rational exponent. 534. (a) 21p (b) 8q4 (c) 436r6In the following exercises, write with a rational exponent. 535. (a) 25a3 (b) 3b (c) 40c10In the following exercises, simplify. 536. (a) 8112 (b) 12513 (c) 6412In the following exercises, simplify. 537. (a) 62514 (b) 24315 (c) 3215In the following exercises, simplify. 538. (a) 1614 (b) 1612 (c) 312515In the following exercises, simplify. 539. (a) 21612 (b) 3215 (c) 8114In the following exercises, simplify. 540. (a) (216)13 (b) 21613 (c) (216)13In the following exercises, simplify. 541. (a) (243)15 (b) 24315 (c) (243)15In the following exercises, simplify. 542. (a) (1)13 (b) 113 (c) (1)13In the following exercises, simplify. 543. (a) (1000)13 (b) 100013 (c) (1000)13In the following exercises, simplify. 544. (a) (81)14 (b) 8114 (c) (81)14In the following exercises, simplify. 545. (a) (49)12 (b) 4912 (c) (49)12In the following exercises, simplify. 546. (a) (36)12 (b) 3612 (c) (36)12In the following exercises, simplify. 547. (a) (1)14 (b) (1)14 (c) 114In the following exercises, simplify. 548. (a) (100)12 (b) 10012 (c) (100)12In the following exercises, simplify. 549. (a) (32)15 (b) (243)15 (c) 12513In the following exercises, write with a rational exponent. 550. (a) m5 (b) n23 (c) p34In the following exercises, write with a rational exponent. 551. (a) r74 (b) s35 (c) t73In the following exercises, write with a rational exponent. 552. (a) u25 (b) v85 (c) w49In the following exercises, write with a rational exponent. 553. (a) a3 (b) b5 (c) c53In the following exercises, simplify. 554. (a) 1632 (b) 823 (c) 10,00034In the following exercises, simplify. 555. (a) 100023 (b) 2532 (c) 3235In the following exercises, simplify. 556. (a) 2753 (b) 1654 (c) 3225In the following exercises, simplify. 557. (a) 1632 (b) 12553 (c) 6443In the following exercises, simplify. 558. (a) 3225 (b) 2723 (c) 2532In the following exercises, simplify. 559. (a) 6452 (b) 8132 (c) 2743In the following exercises, simplify. 560. (a) 2532 (b) 932 (c) (64)23In the following exercises, simplify. 561. (a) 10032 (b) 4952 (c) (100)32In the following exercises, simplify. 562. (a) 932 (b) 932 (c) (9)32In the following exercises, simplify. 563. (a) 6432 (b) 6432 (c) (64)32In the following exercises, simplify. 564. (a) 10032 (b) 10032 (c) (100)32In the following exercises, simplify. 565. (a) 4932 (b) 4932 (c) (49)32In the following exercises, simplify. 566. (a) 4584118 (b) m712m1712 (c) p37p187In the following exercises, simplify. 567. (a) 652612 (b) n210n810 (c) q25p135In the following exercises, simplify. 568. (a) 512572 (b) c34c94 (c) d35d25In the following exercises, simplify. 569. (a )10131053 (b) x56x76 (c) y118y218In the following exercises, simplify. 570. (a) (m6)52 (b) (n9)43 (c) (p 12)34In the following exercises, simplify. 571. (a) (a 12)16 (b) (b 15)35 (c) (c 11)111In the following exercises, simplify. 572. (a) (x 12)23 (b) (y 20)25 (c) (z 16)116In the following exercises, simplify. 573. (a) (h6)43 (b) (k 12)34 (c) (j 10)75In the following exercises, simplify. 574. (a) x72x52 (b) y52y12 (c) r45r95In the following exercises, simplify. 575. (a) s 115s65 (b) z73z13 (c) w27w97In the following exercises, simplify. 576. (a) t 125t75 (b) x32x12 (c) m 138m58In the following exercises, simplify. 577. (a) u 139u49 (b) r 157r87 (c) n35n85In the following exercises, simplify. 578. (a) (9p 2 3 )52 (b) (27q 3 2 )43In the following exercises, simplify. 579. (a) (81r 4 5 )14 (b) (64s 3 7 )16In the following exercises, simplify. 580. (a) (16u 1 3 )34 (b) (100v 2 5 )32In the following exercises, simplify. 581. (a) (27m 3 4 )23 (b) (625n 8 3 )34In the following exercises, simplify. 582. (a) (x8y 10)12 (b) (a9b 12)13In the following exercises, simplify. 583. (a) (r8s4)14 (b) (u 15v 20)15In the following exercises, simplify. 584. (a) (a6b 16)12 (b) (j9k6)23In the following exercises, simplify. 585. (a) (r 16s 10)12 (b) (u 10v5)45In the following exercises, simplify. 586. (a) r52r12r32 (b) s15ss95In the following exercises, simplify. 587. (a) a34a14a 104 (b) b23bb73In the following exercises, simplify. 588. (a) c53c13c23 (b) d35dd25In the following exercises, simplify. 589. (a) m74m54m24 (b) n37nn47In the following exercises, simplify. 590. 452412In the following exercises, simplify. 591. n26n46In the following exercises, simplify. 592. (a 24)16In the following exercises, simplify. 593. (b 10)35In the following exercises, simplify. 594. w25w75In the following exercises, simplify. 595. z23z83In the following exercises, simplify. 596. (27r 3 5 )13In the following exercises, simplify. 597. (64s 3 5 )16In the following exercises, simplify. 598. (r9s 12)13In the following exercises, simplify. 599. (u 12v 18)16Landscaping Joe wants to have a square garden plot in his backyard. He has enough compost to cover an area of 144 square feet. Simplify 14412 to find the length of each side of his garden.Landscaping Elliott wants to make a square patio in his yard. He has enough concrete to pave an area of 242 square feet. Simplify 24212 to find the length of each side of his patio. Round to the nearest tenth of a foot.Gravity While putting up holiday decorations, Bob dropped a decoration from the top of a tree that is 12 feet tall. Simplify 12121612 to find how many seconds it took for the decoration to reach the ground. Round to the nearest tenth of a second.Gravity An airplane dropped a flare from a height of 1024 feet above a lake. Simplify 1024121612 to find how many seconds it took for the flare to reach the water.Show two different algebraic methods to simplify 432 . Explain all your steps.Explain why the expression (16)32 cannot be evaluated.In the following exercises, simplify. 606. 64In the following exercises, simplify. 607. 144In the following exercises, simplify. 608. 25In the following exercises, simplify. 609. 81In the following exercises, simplify. 610. 9In the following exercises, simplify. 611. 36In the following exercises, simplify. 612. 64+225In the following exercises, simplify. 613. 64+225In the following exercises, estimate each square root between two consecutive whole numbers. 614. 28In the following exercises, estimate each square root between two consecutive whole numbers. 615. 155In the following exercises, approximate each square root and round to two decimal places. 616. 15In the following exercises, approximate each square root and round to two decimal places. 617. 57In the following exercises, simplify. 618. q2In the following exercises, simplify. 619. 64b2In the following exercises, simplify. 620. 121a2In the following exercises, simplify. 621. 225m2n2In the following exercises, simplify. 622. 100q2In the following exercises, simplify. 623. 49y2In the following exercises, simplify. 624. 4a2b2In the following exercises, simplify. 625. 121c2d2In the following exercises, simplify. 626. 300In the following exercises, simplify. 627. 98In the following exercises, simplify. 628. x13In the following exercises, simplify. 629. y19In the following exercises, simplify. 630. 16m4In the following exercises, simplify. 631. 36n13In the following exercises, simplify. 632. 288m21In the following exercises, simplify. 633. 150n7In the following exercises, simplify. 634. 48r5s4In the following exercises, simplify. 635. 108r5s3In the following exercises, simplify. 636. 10505In the following exercises, simplify. 637. 6+726In the following exercises, simplify. 638. 1625In the following exercises, simplify. 639. 8136In the following exercises, simplify. 640. x8x4In the following exercises, simplify. 641. y6y2In the following exercises, simplify. 642. 98p62p2In the following exercises, simplify. 643. 72q82q4In the following exercises, simplify. 644. 65121In the following exercises, simplify. 645. 26169In the following exercises, simplify. 646. 64x425x2In the following exercises, simplify. 647. 36r 1016r5In the following exercises, simplify. 648. 48p3q527pqIn the following exercises, simplify. 649. 12r5s775r2sIn the following exercises, simplify. 650. 32+2In the following exercises, simplify. 651. 55+75In the following exercises, simplify. 652. 4y+4yIn the following exercises, simplify. 653. 6m2mIn the following exercises, simplify. 654. 37+277In the following exercises, simplify. 655. 813+23+313In the following exercises, simplify. 656. 35xy5xy+35xyIn the following exercises, simplify. 657. 23rs+3rs5rsIn the following exercises, simplify. 658. 32+32In the following exercises, simplify. 659. 8+32In the following exercises, simplify. 660. 72+50In the following exercises, simplify. 661. 48+75In the following exercises, simplify. 662. 332+98In the following exercises, simplify. 663. 132718192In the following exercises, simplify. 664. 50y572y5In the following exercises, simplify. 665. 618n438n4+n250In the following exercises, simplify. 666. 220In the following exercises, simplify. 667. 22614In the following exercises, simplify. 668. 2m220m4In the following exercises, simplify. 669. (62y)(350y3)In the following exercises, simplify. 670. (63v4)(530v)In the following exercises, simplify. 671. (8)2In the following exercises, simplify. 672. ( 10)2In the following exercises, simplify. 673. (25)(55)In the following exercises, simplify. 674. (33)(518)In the following exercises, simplify. 675. 10(27)In the following exercises, simplify. 676. 3(4+12)In the following exercises, simplify. 677. (5+2)(32)In the following exercises, simplify. 678. (537)(127)In the following exercises, simplify. 679. (13x)(5+2x)In the following exercises, simplify. 680. (3+4y)(10y)In the following exercises, simplify. 681. (1+6p)2In the following exercises, simplify. 682. (265)2In the following exercises, simplify. 683. (3+27)(327)In the following exercises, simplify. 684. (611)(6+11)In the following exercises, simplify. 685. 7510In the following exercises, simplify. 686. 2126In the following exercises, simplify. 687. 4827In the following exercises, simplify. 688. 75x73x3In the following exercises, simplify. 689. 20y52yIn the following exercises, simplify. 690. 98p6q42p4q8In the following exercises, rationalize the denominator. 691. 1015