Question

Help please! I don’t get the question

Answer 1

Option B:

$9^{\frac{1}{8}x}$ is the equivalent expression to the given expression.

Solution:

Given expression:

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

To find the equivalent expression to the given expression.

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

Using radical rule: $\sqrt[n]{a}=a^{\frac{1}{n}}$

So that $\sqrt[4]{9} = 9^{\frac{1}{4} }$.

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

Using exponent rule: $\left(a^{b}\right)^{c}=a^{b c}$

         $=9^{\frac{1}{4} \cdot \frac{1}{2} x}$

         $=9^{\frac{1}{8}x}$

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

Hence $9^{\frac{1}{8}x}$ is the equivalent expression to the given expression.

Option B is the correct answer.