Question

Simplify the expression ${\left(x^{\sqrt{5}}\right)}^{\sqrt{3}}$.

Short answer

The simplified value of expression is $x^{\sqrt{15}}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is ${\left(x^{\sqrt{5}}\right)}^{\sqrt{3}}$.

Step 2. Simplify the expression.

The given expression ${\left(x^{\sqrt{5}}\right)}^{\sqrt{3}}$is simplified as:

$\begin{array}{l}{\left(x^{\sqrt{5}}\right)}^{\sqrt{3}}={\left(x\right)}^{\sqrt{5}\times \sqrt{3}}\\ ={\left(x\right)}^{\sqrt{15}}\\ =x^{\sqrt{15}}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $x^{\sqrt{15}}$.