Question

Create an equivalent expression of the photo.

( / is a fraction)


A: 1.6 power of 4 / 1.7 power of 3

B: 1.7 power of 28 / 1.6 power of 21

C: 1.7 power of 3 / 1.6 power of 4

D: 1.6 power of 21 / 1.7 power of 28

Answer 1

B: 1.7 power of 28 / 1.6 power of 21

Explanation:

You want to know what expression is equivalent to (1.6^3/1.7^4)^-7.

Rules of exponents

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

a^-b = 1/a^b

Application

The expression can be simplified as follows.

`\left((1.6^3)/(1.7^4)\right)^(-7)=(1.6^(3(-7)))/(1.7^(4(-7)))=(1.6^(-21))/(1.7^(-28))=\boxed{(1.7^(28))/(1.6^(21))}`

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