Question

write the following as an exponential expression.
\sqrt8{x^{7}}

Explanation:

Step1: Recall root-to-exponent rule

The nth root of a term equals the term raised to $\frac{1}{n}$, so $\sqrt[n]{a} = a^{\frac{1}{n}}$.

Step2: Apply rule to the given root

Here, $n=8$ and the term is $x^7$, so substitute into the rule:
$\sqrt[8]{x^7} = (x^7)^{\frac{1}{7}}$

Step3: Simplify using exponent power rule

Use $(a^m)^n = a^{m \times n}$:
$(x^7)^{\frac{1}{8}} = x^{7 \times \frac{1}{8}} = x^{\frac{7}{8}}$

Answer:

$x^{\frac{7}{8}}$