Solve by Factoring x^(1/4)=3

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

Step 1

Subtract $3$ from both sides of the equation.

$x^{\frac{1}{4}} - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

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

Step 3

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

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

Step 4

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{1}{4}})}^{4}$ .

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{1} = 3^{4}$

Simplify.

$x = 3^{4}$

Simplify the right side.

Raise $3$ to the power of $4$ .

$x = 81$