Problem 1SP Problem 2SP Problem 3SP Problem 4SP Problem 5SP: Convert the expression to radical form and simplify, if possible. 64 − 1 / 3 Problem 6SP Problem 7SP Problem 8SP Problem 9SP Problem 10SP Problem 11SP: Convert each expression to radical notation. Assume all variables represent positive real numbers. t... Problem 12SP: Convert each expression to radical notation. Assume all variables represent positive real numbers. 2... Problem 13SP: Convert each expression to radical notation. Assume all variables represent positive real... Problem 14SP: Convert each expression to radical notation. Assume all variables represent positive real... Problem 15SP: Convert to an equivalent expression rational exponents. Assume all variables represent positive real... Problem 16SP Problem 17SP Problem 18SP: Use the properties of exponents to simplify the expressions. Assume all variables represent positive... Problem 19SP: Use the properties of exponents to simplify the expressions. Assume all variables represent positive... Problem 20SP: Use the properties of exponents to simplify the expressions. Assume all variables represent positive... Problem 21SP: The formula for the radius of a sphere is r = ( 3 V 4 π ) 1 / 3 where V is the volume. Find the... Problem 1PE Problem 2PE: Given 27 3 , identify the index and radicand. Problem 3PE: For Exercises 3–6, evaluate the radicals. 25 Problem 4PE: For Exercises 3–6, evaluate the radicals. 8 3 Problem 5PE: For Exercises 3–6, evaluate the radicals. 81 4 Problem 6PE: For Exercises 3–6, evaluate the radicals. ( 16 4 ) 3 Problem 7PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.)
7.
Problem 8PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) 16 1 / 4 Problem 9PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) − 144 1 /... Problem 10PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) − 16 1 /... Problem 11PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) ( − 144 )... Problem 12PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) ( − 16 )... Problem 13PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.)
13.
Problem 14PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) ( − 32 )... Problem 15PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) 25 − 1 /... Problem 16PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) 27 − 1/3 Problem 17PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.)
17.
Problem 18PE: For Exercises 7–18, convert the expressions to radical form and simplify. (See Example 1.) − 64 − 1... Problem 19PE: Explain how to interpret the expression a m / n as a radical. Problem 20PE: 20. Explain why is easier to evaluate than.
Problem 21PE: For Exercises 21–24, simplify the expression, if possible. (See Example 2.)
21. a.
b.
c.
d.... Problem 22PE: For Exercises 21–24, simplify the expression, if possible. (See Example 2.)
22. a.
b.
c. ... Problem 23PE: For Exercises 21–24, simplify the expression, if possible. (See Example... Problem 24PE: For Exercises 21–24, simplify the expression, if possible. (See Example 2.) a. 4 3 / 2 b. − 4 3 / 2... Problem 25PE: For Exercises 25–48, simplify the expression. (See Example 2.) 64 − 3 / 2 Problem 26PE: For Exercises 25–48, simplify the expression. (See Example 2.) 81 − 3 / 2 Problem 27PE: For Exercises 25–48, simplify the expression. (See Example 2.)
27.
Problem 28PE: For Exercises 25–48, simplify the expression. (See Example 2.) 1 5 / 3 Problem 29PE: For Exercises 25–48, simplify the expression. (See Example 2.)
29.
Problem 30PE: For Exercises 25–48, simplify the expression. (See Example 2.) − 16 − 5 / 4 Problem 31PE: For Exercises 25–48, simplify the expression. (See Example 2.)
31.
Problem 32PE: For Exercises 25–48, simplify the expression. (See Example 2.) ( 49 100 ) − 1 / 2 Problem 33PE: For Exercises 25–48, simplify the expression. (See Example 2.)
33.
Problem 34PE: For Exercises 25–48, simplify the expression. (See Example 2.) ( − 49 ) − 3 / 2 Problem 35PE: For Exercises 25–48, simplify the expression. (See Example 2.) ( − 8 ) 1 / 3 Problem 36PE: For Exercises 25–48, simplify the expression. (See Example 2.)
36.
Problem 37PE: For Exercises 25–48, simplify the expression. (See Example 2.)
37.
Problem 38PE: For Exercises 25–48, simplify the expression. (See Example 2.) − 9 1 / 2 Problem 39PE: For Exercises 25–48, simplify the expression. (See Example 2.) 1 36 − 1 / 2 Problem 40PE: For Exercises 25–48, simplify the expression. (See Example 2.) 1 16 − 1 / 2 Problem 41PE: For Exercises 25–48, simplify the expression. (See Example 2.)
41.
Problem 42PE: For Exercises 25–48, simplify the expression. (See Example 2.) 1 81 − 3 / 4 Problem 43PE: For Exercises 25–48, simplify the expression. (See Example 2.) ( 1 8 ) 2 / 3 + ( 1 4 ) 1 / 2 Problem 44PE: For Exercises 25–48, simplify the expression. (See Example 2.) ( 1 8 ) − 2 / 3 + ( 1 4 ) − 1 / 2 Problem 45PE: For Exercises 25–48, simplify the expression. (See Example 2.) ( 1 16 ) − 3 / 4 − ( 1 49 ) − 1 / 2 Problem 46PE: For Exercises 25–48, simplify the expression. (See Example 2.) ( 1 16 ) 1 / 4 − ( 1 49 ) 1 / 2 Problem 47PE: For Exercises 25–48, simplify the expression. (See Example 2.) ( 1 4 ) 1 / 2 + ( 1 64 ) − 1 / 3 Problem 48PE: For Exercises 25–48, simplify the expression. (See Example 2.)
48.
Problem 49PE: For Exercises 49–56, convert each expression to radical notation. (See Example 3.) q 2 / 3 Problem 50PE: For Exercises 49–56, convert each expression to radical notation. (See Example 3.) t 3 / 5 Problem 51PE: For Exercises 49–56, convert each expression to radical notation. (See Example 3.)
51.
Problem 52PE: For Exercises 49–56, convert each expression to radical notation. (See Example 3.) 8 b 4 / 9 Problem 53PE: For Exercises 49–56, convert each expression to radical notation. (See Example 3.) x 2 / 3 y 1 / 3 Problem 54PE: For Exercises 49–56, convert each expression to radical notation. (See Example 3.)
54.
Problem 55PE: For Exercises 49–56, convert each expression to radical notation. (See Example 3.) 6 r − 2 / 5 Problem 56PE: For Exercises 49–56, convert each expression to radical notation. (See Example 3.) 7 x − 3 / 4 Problem 57PE: For Exercises 57–64, write each expression by using rational exponents rather than radical notation.... Problem 58PE: For Exercises 57–64, write each expression by using rational exponents rather than radical notation.... Problem 59PE: For Exercises 57–64, write each expression by using rational exponents rather than radical notation.... Problem 60PE: For Exercises 57–64, write each expression by using rational exponents rather than radical notation.... Problem 61PE: For Exercises 57–64, write each expression by using rational exponents rather than radical notation.... Problem 62PE: For Exercises 57–64, write each expression by using rational exponents rather than radical notation.... Problem 63PE: For Exercises 57–64, write each expression by using rational exponents rather than radical notation.... Problem 64PE Problem 65PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 66PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 67PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 68PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 69PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 70PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 71PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 72PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 73PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 74PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 75PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 76PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 77PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 78PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 79PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 80PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 81PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 82PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 83PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 84PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 85PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 86PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 87PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 88PE: For Exercises 65–88, simplify the expressions by using the properties of rational exponents. Write... Problem 89PE: 89. If P dollars in principal grows to A dollars after t years with annual interest, then the... Problem 90PE: If the area A of a square is known, then the length of its sides, s, can be computed by the formula... Problem 91PE: The radius r of a sphere of volume V is given by r = ( 3 V 4 π ) 1 / 3 . Find the radius of a... Problem 92PE: Is ( a + b ) 1 / 2 the same as a 1 / 2 + b 1 / 2 ? If not, give a counterexample. Problem 93PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 94PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 95PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 96PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 97PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 98PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 99PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 100PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 101PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 102PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 103PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 104PE: For Exercises 93–104, write the expression using rational exponents. Then simplify and convert back... Problem 105PE: For Exercises 105–108, write the expression as a single radical. x 3 Problem 106PE: For Exercises 105–108, write the expression as a single radical. x 3 Problem 107PE: For Exercises 105–108, write the expression as a single radical. w 3 5 Problem 108PE: For Exercises 105–108, write the expression as a single radical. w 4 3 Problem 109PE: For Exercises 109–116, use a calculator to approximate the expressions. Round to four decimal... Problem 110PE: For Exercises 109–116, use a calculator to approximate the expressions. Round to four decimal... Problem 111PE: For Exercises 109–116, use a calculator to approximate the expressions. Round to four decimal... Problem 112PE: For Exercises 109–116, use a calculator to approximate the expressions. Round to four decimal... Problem 113PE: For Exercises 109–116, use a calculator to approximate the expressions. Round to four decimal... Problem 114PE: For Exercises 109–116, use a calculator to approximate the expressions. Round to four decimal... Problem 115PE: For Exercises 109–116, use a calculator to approximate the expressions. Round to four decimal... Problem 116PE: For Exercises 109–116, use a calculator to approximate the expressions. Round to four decimal... format_list_bulleted