Simplify the Radical Expression ((x^8)/(x^6))^(5/4)

${(\frac{x^{8}}{x^{6}})}^{\frac{5}{4}}$

Step 1

Cancel the common factor of $x^{8}$ and $x^{6}$ .

Factor $x^{6}$ out of $x^{8}$ .

${(\frac{x^{6} x^{2}}{x^{6}})}^{\frac{5}{4}}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{x^{6} x^{2}}{x^{6} \cdot 1})}^{\frac{5}{4}}$

Cancel the common factor.

${(\frac{x^{6} x^{2}}{x^{6} \cdot 1})}^{\frac{5}{4}}$

Rewrite the expression.

${(\frac{x^{2}}{1})}^{\frac{5}{4}}$

Divide $x^{2}$ by $1$ .

${(x^{2})}^{\frac{5}{4}}$

Step 2

Multiply the exponents in ${(x^{2})}^{\frac{5}{4}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{2 (\frac{5}{4})}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x^{2 \frac{5}{2 (2)}}$

Cancel the common factor.

$x^{2 \frac{5}{2 \cdot 2}}$

Rewrite the expression.

$x^{\frac{5}{2}}$