Simplify (81m^6)^(1/2)

${(81 m^{6})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $81 m^{6}$ .

$81^{\frac{1}{2}} {(m^{6})}^{\frac{1}{2}}$

Rewrite $81$ as $9^{2}$ .

${(9^{2})}^{\frac{1}{2}} {(m^{6})}^{\frac{1}{2}}$

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

$9^{2 (\frac{1}{2})} {(m^{6})}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$9^{2 (\frac{1}{2})} {(m^{6})}^{\frac{1}{2}}$

Rewrite the expression.

$9^{1} {(m^{6})}^{\frac{1}{2}}$

Step 3

Simplify the expression.

Evaluate the exponent.

$9 {(m^{6})}^{\frac{1}{2}}$

Multiply the exponents in ${(m^{6})}^{\frac{1}{2}}$ .

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

$9 m^{6 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$9 m^{2 (3) \frac{1}{2}}$

Cancel the common factor.

$9 m^{2 \cdot 3 \frac{1}{2}}$

Rewrite the expression.

$9 m^{3}$