Simplify (81x^8)^(1/2)

${(81 x^{8})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $81 x^{8}$ .

$81^{\frac{1}{2}} {(x^{8})}^{\frac{1}{2}}$

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

${(9^{2})}^{\frac{1}{2}} {(x^{8})}^{\frac{1}{2}}$

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

$9^{2 (\frac{1}{2})} {(x^{8})}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$9^{2 (\frac{1}{2})} {(x^{8})}^{\frac{1}{2}}$

Rewrite the expression.

$9^{1} {(x^{8})}^{\frac{1}{2}}$

Step 3

Simplify the expression.

Evaluate the exponent.

$9 {(x^{8})}^{\frac{1}{2}}$

Multiply the exponents in ${(x^{8})}^{\frac{1}{2}}$ .

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

$9 x^{8 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factor.

$9 x^{2 \cdot 4 \frac{1}{2}}$

Rewrite the expression.

$9 x^{4}$