Question

Which of these answer choices show a pair of equivalent expressions?

Answer 1

A and B

Explanation:

With exponents, we will take what is in the numerator and raise the base to that power and then take what is in the denominator and root the base to that.

as an example

`2 ^(4)/(5) = (\sqrt[5]{2})^4` The base here is 2 in the exponent we have a 4 which means the base will be raised to the 4th power and in the denominator we have a 5 which means we must put the 2 to the 5th root.

Now we can look through the choice to see where this rule follows.

A) The base is 125 and has 9 in the numerator and 3 in the denominator.

So this does seem to follow the rule power 9 root 3

B) base 8, 9 in the numerator and 2 in denominator. This does follow the rule power 9 root 2

C) Base 12 numerator 2 and denominator 7, so this should be root 7 power 2 but it is flipped so this is incorrect

D) base 4 numerator 1 and denominator 5, so this should be power 1 root 5, this is also flipped so incorrect