Question

Which of these choices show a pair of equivalent expressions? Check all that apply.

Answer 1

Only the following pairs:

`( \sqrt[4]{81})^5 = 81^(5/4) 5^(3/2) = ( √(5))^3`

Answer 2

`\bf a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{( n)/( m)}\\\\ -------------------------------`


`\bf \left( \sqrt[4]{81} \right)^5\implies \sqrt[4]{81^5}\implies 81^{(5)/(4)}\quad \checkmark \\\\\\ 7^{(5)/(7)}\implies \sqrt[7]{7^5}\implies \left( \sqrt[7]{7} \right)^5\quad \otimes \\\\\\ 6^{(2)/(7)}\implies \sqrt[7]{6^2}\implies \left( \sqrt[7]{6} \right)^2\quad \otimes \\\\\\ 5^{(3)/(2)}\implies \sqrt[2]{5^3}\implies \left( √(5) \right)^3\quad \checkmark`