Evaluate (81x)^(1/4)

${(81 x)}^{\frac{1}{4}}$

Step 1

Simplify the expression.

Apply the product rule to $81 x$ .

$81^{\frac{1}{4}} x^{\frac{1}{4}}$

Rewrite $81$ as $3^{4}$ .

${(3^{4})}^{\frac{1}{4}} x^{\frac{1}{4}}$

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

$3^{4 (\frac{1}{4})} x^{\frac{1}{4}}$

Step 2

Cancel the common factor of $4$ .

Cancel the common factor.

$3^{4 (\frac{1}{4})} x^{\frac{1}{4}}$

Rewrite the expression.

$3^{1} x^{\frac{1}{4}}$

Step 3

Evaluate the exponent.

$3 x^{\frac{1}{4}}$