which is equivalent to $sqrt3{8^{x}}$?\n$sqrtx{8^{3}}$\n$8^{\frac{3}{x}}$\n$8^{\frac{x}{3}}$\n$8^{3x}$
which is equivalent to $sqrt3{8^{x}}$?\n$sqrtx{8^{3}}$\n$8^{\frac{3}{x}}$\n$8^{\frac{x}{3}}$\n$8^{3x}$
Answer
Explanation:
Step1: Recall radical - exponent conversion rule
The n - th root of a number (a) can be written as (a^{\frac{1}{n}}). So, (\sqrt[3]{8^{x}}=(8^{x})^{\frac{1}{3}}).
Step2: Apply power - of - a - power rule
The power - of - a - power rule ((a^{m})^{n}=a^{mn}). Here, (a = 8), (m=x), and (n=\frac{1}{3}). Then ((8^{x})^{\frac{1}{3}}=8^{x\times\frac{1}{3}}=8^{\frac{x}{3}}).
Answer:
(8^{\frac{x}{3}}) (the third option)