Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in re…

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.

Question

Chapter 5.2, Problem 37WE

To determine

To find: Simplify the given expression.

Expert Solution & Answer

Answer to Problem 37WE

(x2y−1)−2(y2x−1)2=y2x2

Explanation of Solution

Given information:

(x2y−1)−2(y2x−1)2

Concept:

ab⋅cd=a⋅cb⋅d

Using law of exponents

a−m=1amam⋅an=am+naman=am−na0=1

(an)m=amn

Where a be any value.

(x2y−1)−2(y2x−1)2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = ( x 2 ) −2 ( y −1 ) −2 ⋅ ( y 2 ) 2 ( x −1 ) 2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = x 2×( −2 ) y ( −1 )×( −2 ) ⋅ y 2×2 x ( −1 )×2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = x −4 y 2 ⋅ y 4 x −2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = x −4 x −2 ⋅ y 4 y 2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = x −4−( −2 ) ⋅ y 4−2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = x −4+2 ⋅ y 2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = x −2 ⋅ y 2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = 1 x 2 ⋅ y 2

⇒ ( x 2 y −1 ) −2 ( y 2 x −1 ) 2 = y 2 x 2

Therefore,

(x2y−1)−2(y2x−1)2=y2x2

Chapter 5.2, Problem 36WE

Chapter 5.2, Problem 38WE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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