Simplify ((x-5)^(3/2))^(2/3)

${({(x - 5)}^{\frac{3}{2}})}^{\frac{2}{3}}$

Step 1

Multiply the exponents in ${({(x - 5)}^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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

${(x - 5)}^{\frac{3}{2} \cdot \frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x - 5)}^{\frac{3}{2} \cdot \frac{2}{3}}$

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(x - 5)}^{1}$

Step 2

Simplify.

$x - 5$