Solve for y y^(1/4)=2

$y^{\frac{1}{4}} = 2$

Step 1

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

${(y^{\frac{1}{4}})}^{4} = 2^{4}$

Step 2

Simplify the exponent.

Simplify the left side.

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

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

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

$y^{\frac{1}{4} \cdot 4} = 2^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$y^{\frac{1}{4} \cdot 4} = 2^{4}$

Rewrite the expression.

$y^{1} = 2^{4}$

Simplify.

$y = 2^{4}$

Simplify the right side.

Raise $2$ to the power of $4$ .

$y = 16$