Question

Which is equivalent to RootIndex 4 StartRoot 9 EndRoot Superscript one-half x?

Answer 1

Answer:

${9}^ {\frac{1}{8}x}$

Step-by-step explanation:

We want to find an equivalent expression for

$(\sqrt[4]{9})^{ \frac{1}{2}x}$

To find an equivalent expression, we need to apply the following property of exponents:

${a}^{ \frac{m}{n}}=( \sqrt[n]{ {a}} )^{m}$

We let a=9, n=4 and m=½x

Then :

${9}^{ \frac{ \frac{1}{2}x}{4}}=( \sqrt[4]{ {9}} )^{ \frac{1}{2}x}$

Simplify the left hand side to get:

${9}^ {\frac{1}{8}x} =( \sqrt[4]{ {9}} )^{ \frac{1}{2}x}$

Therefore the correct answer is:

${9}^ {\frac{1}{8}x}$