Simplify (u^4*u^-2)^(5/2)

${(u^{4} \cdot u^{- 2})}^{\frac{5}{2}}$

Step 1

Multiply $u^{4}$ by $u^{- 2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(u^{4 - 2})}^{\frac{5}{2}}$

Subtract $2$ from $4$ .

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

Step 2

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$u^{5}$