Simplify (9u^2)^(3/2)

${(9 u^{2})}^{\frac{3}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $9 u^{2}$ .

$9^{\frac{3}{2}} {(u^{2})}^{\frac{3}{2}}$

Rewrite $9$ as $3^{2}$ .

${(3^{2})}^{\frac{3}{2}} {(u^{2})}^{\frac{3}{2}}$

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

$3^{2 (\frac{3}{2})} {(u^{2})}^{\frac{3}{2}}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$3^{2 (\frac{3}{2})} {(u^{2})}^{\frac{3}{2}}$

Rewrite the expression.

$3^{3} {(u^{2})}^{\frac{3}{2}}$

Step 3

Simplify the expression.

Raise $3$ to the power of $3$ .

$27 {(u^{2})}^{\frac{3}{2}}$

Multiply the exponents in ${(u^{2})}^{\frac{3}{2}}$ .

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

$27 u^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$27 u^{2 (\frac{3}{2})}$

Rewrite the expression.

$27 u^{3}$