Question

Which is equivalent to 3sqrt8^x?

Answer 1

Answer:

$8^{\frac{x}{3} }$ is the correct option.

Step-by-step explanation:

Here is the correct question: Which is equivalent to ∛8^x?

• $\sqrt[x]{8^{3} }$
• $8^{\frac{3}{x} }$
• $8^{\frac{x}{3} }$
• $8^{3x}$

As per rule; while writing exponent into fraction form, Power is considered as numerator and Root as denominator, however base remain same.

∴ For writing exponent to fraction: $\sqrt[root]{base^{Power} } = base^{\frac{Power}{root} }$

Now, writing given exponent to fraction.

$\sqrt[3]{8^{x} } = 8^{\frac{x}{3}}$

Hence, $8^{\frac{x}{3} }$ is the correct option.