which of these choices show a pair equivalent expressions? Check all that apply. A. 12^7/2 and (sqrt 12)^7 B. 8^2/29 and (sqrt 8)^9 C. (3sqrt 125)^7 and 125^7/3 D.4^1/5 and (sqrt 4)^5

**Answer:**

Hi Phyllis,

You asked which of the following are equivalent expressions,

A)127/2and(12−−√)7B)82/29and(8–√)9C)1257/3and3(125−−−√)7/3D)41/5and(4–√)5

There is a law in mathematics that says, am−−−√n=a(m/n), using this we can change all of the square roots into fractional exponents.

Doing this we get,

(12−−√)7=12(7/2)(8–√)9=8(9/2)3×(125−−−√)(7/3)=3×125(7/6)(4–√)5=4(5/2)

we can now take another look at the pairs of numbers and see which ones are equivalent,

A)127/2and127/2B)82/29and89/2C)3×1257/3and3×1257/6D)41/5and45/2

As you can see the answer is A

Alternatively you could always just plug these numbers into a calculator and get a decimal approximation and compare them that way