Question

Which is equivalent to 5√1,215^x?

A)243x
B)1,215^1/5x
C)1,215^1/5x
D)243^1/x

Answer 1

$\sqrt[n]{a^m}=a^\frac{m}{n}$

$\sqrt[5]{1,215^x}=1,215^\frac{x}{5}=1,215^{\frac{1}{5}x}$

Answer: B)?C)? 1,215^1/5 x

Answer 2

Answer:

Option C is correct

The expression $(1215)^{\frac{1}{5}x}$  is equivalent to $\sqrt[5]{1215^x}$

Step-by-step explanation:

Simplify the radical Expression: $\sqrt[5]{1215^x}$

A radical expression can be written by using the exponents and also using the following procedure:

$\sqrt[n]{x} = x^{\frac{1}{n}}$

when x be non-negative then n can be any index

when x is negative, then n can be odd.

The following radical expression can be written as:

$\sqrt[5]{1215^x} = (1215^x)^{\frac{1}{5}}$ = $(1215)^{\frac{1}{5}x}$

Therefore, the expression $(1215)^{\frac{1}{5}x}$  is equivalent to $\sqrt[5]{1215^x}$