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olga55 [171]
3 years ago
7

Help please! I don’t get the question

Mathematics
1 answer:
Vlad [161]3 years ago
8 0

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.

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