Question

Please help.. I will give points

Answer 1

Let us check each option

A. $8^{9/2} and (\sqrt{8})^{9}$

these are equivalent

B. $(\sqrt[3]{125} )^9 and 125^{9/3}$

these are equivalent

C. $12^{2/7} and (\sqrt{12})^7$

these are not equivalent

D. $4^{1/5} and (\sqrt{4})^5$

these are not equivalent

Answer 2

A. 8^9/2= around 11585.2375; (sqrt8)^9= around 11585.2375. So choice A shows a pair of equivalent expressions.

B. (3sqrt125)^9=1,953,125; 125^9/3=1,953,125. So choice B also shows a pair of equivalent expressions.

C. 12^2/7= around 2.03394; (sqrt12)^7= around 5,985.96759. So choice C does not show a pair of equivalent expressions.

D. 4^1/5=around 1.31951; (sqrt4)^5=32. So choice D also doesn't show a pair of equivalent expressions.

Your answers are A and B.

I hope this helps ;)