Solve for y fourth root of y+2+9=14

$\sqrt[4]{y + 2} + 9 = 14$

Step 1

Move all terms not containing $\sqrt[4]{y + 2}$ to the right side of the equation.

Subtract $9$ from both sides of the equation.

$\sqrt[4]{y + 2} = 14 - 9$

Subtract $9$ from $14$ .

$\sqrt[4]{y + 2} = 5$

Step 2

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{y + 2}}^{4} = 5^{4}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{y + 2}$ as ${(y + 2)}^{\frac{1}{4}}$ .

${({(y + 2)}^{\frac{1}{4}})}^{4} = 5^{4}$

Simplify the left side.

Simplify ${({(y + 2)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(y + 2)}^{\frac{1}{4}})}^{4}$ .

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

${(y + 2)}^{\frac{1}{4} \cdot 4} = 5^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(y + 2)}^{\frac{1}{4} \cdot 4} = 5^{4}$

Rewrite the expression.

${(y + 2)}^{1} = 5^{4}$

Simplify.

$y + 2 = 5^{4}$

Simplify the right side.

Raise $5$ to the power of $4$ .

$y + 2 = 625$

Step 4

Move all terms not containing $y$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$y = 625 - 2$

Subtract $2$ from $625$ .

$y = 623$