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

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

Step 1

Apply the distributive property.

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

Step 2

Combine $x$ and $\frac{3}{2}$ .

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

Step 3

Multiply $- 5 (\frac{3}{2})$ .

Combine $- 5$ and $\frac{3}{2}$ .

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

Multiply $- 5$ by $3$ .

${(\frac{x \cdot 3}{2} + \frac{- 15}{2})}^{\frac{2}{3}}$

Step 4

Simplify each term.

Move $3$ to the left of $x$ .

${(\frac{3 \cdot x}{2} + \frac{- 15}{2})}^{\frac{2}{3}}$

Move the negative in front of the fraction.

${(\frac{3 x}{2} - \frac{15}{2})}^{\frac{2}{3}}$