Simplify the Radical Expression (9r^4)^(1/2)

${(9 r^{4})}^{\frac{1}{2}}$

Apply the product rule to $9 r^{4}$ .

$9^{\frac{1}{2}} {(r^{4})}^{\frac{1}{2}}$

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

${(3^{2})}^{\frac{1}{2}} {(r^{4})}^{\frac{1}{2}}$

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

$3^{2 (\frac{1}{2})} {(r^{4})}^{\frac{1}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3^{2 (\frac{1}{2})} {(r^{4})}^{\frac{1}{2}}$

Rewrite the expression.

$3^{1} {(r^{4})}^{\frac{1}{2}}$

Evaluate the exponent.

$3 {(r^{4})}^{\frac{1}{2}}$

Multiply the exponents in ${(r^{4})}^{\frac{1}{2}}$ .

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

$3 r^{4 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$3 r^{2 (2) \frac{1}{2}}$

Cancel the common factor.

$3 r^{2 \cdot 2 \frac{1}{2}}$

Rewrite the expression.

$3 r^{2}$