Question

Rewrite the rational exponent as a radical by extending the properties of integer exponents. (2 points)

2 to the 7 over 8 power, all over 2 to the 1 over 4 power

Answer 1

7/2^5

So in letter answer C

Answer 2

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}} \\\\\\ a^{-{ n}} \implies \cfrac{1}{a^( n)}\qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}}\\\\ -----------------------------\\\\`


`\bf \cfrac{2^{(7)/(8)}}{2^{(1)/(4)}}\implies \cfrac{2^{(7)/(8)}}{1}\cdot \cfrac{1}{2^{(1)/(4)}}\implies 2^{(7)/(8)}\cdot 2^{-(1)/(4)}\impliedby \begin{array}{llll} \textit{same base}\\ \textit{add the exponents} \end{array} \\\\\\ 2^{\cfrac{}{}(7)/(8)-(1)/(4)}\implies 2^{(5)/(8)}\implies \sqrt[8]{2^5}\implies \sqrt[8]{32}`