Answer:
[tex]{9}^ {\frac{1}{8}x}[/tex]
Step-by-step explanation:
We want to find an equivalent expression for
[tex] (\sqrt[4]{9})^{ \frac{1}{2}x} [/tex]
To find an equivalent expression, we need to apply the following property of exponents:
[tex] {a}^{ \frac{m}{n}}=( \sqrt[n]{ {a}} )^{m} [/tex]
We let a=9, n=4 and m=½x
Then :
[tex] {9}^{ \frac{ \frac{1}{2}x}{4}}=( \sqrt[4]{ {9}} )^{ \frac{1}{2}x} [/tex]
Simplify the left hand side to get:
[tex]{9}^ {\frac{1}{8}x} =( \sqrt[4]{ {9}} )^{ \frac{1}{2}x} [/tex]
Therefore the correct answer is:
[tex]{9}^ {\frac{1}{8}x}[/tex]
