which is equivalent to $sqrt5{1,215^{x}}$?\n$243^{x}$\n$1,215^{\frac{1}{5}x}$\n$1,215^{\frac{1}{5x}}$\n$243^{…

which is equivalent to $sqrt5{1,215^{x}}$?\n$243^{x}$\n$1,215^{\frac{1}{5}x}$\n$1,215^{\frac{1}{5x}}$\n$243^{\frac{1}{x}}$

which is equivalent to $sqrt5{1,215^{x}}$?\n$243^{x}$\n$1,215^{\frac{1}{5}x}$\n$1,215^{\frac{1}{5x}}$\n$243^{\frac{1}{x}}$

Answer

Explanation:

Step1: Recall the radical - exponent rule

The $n$-th root of a number $a$ can be written as $a^{\frac{1}{n}}$. So, $\sqrt[5]{1215^{x}}=(1215^{x})^{\frac{1}{5}}$.

Step2: Apply the power - of - a - power rule

The power - of - a - power rule states that $(a^{m})^{n}=a^{mn}$. Here, $a = 1215$, $m=x$, and $n=\frac{1}{5}$. So, $(1215^{x})^{\frac{1}{5}}=1215^{\frac{1}{5}x}$.

Answer:

$1215^{\frac{1}{5}x}$