Solve the Rational Equation for s fourth root of 2s+10=4

$\sqrt[4]{2 s + 10} = 4$

Step 1

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

${\sqrt[4]{2 s + 10}}^{4} = 4^{4}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2 s + 10}$ as ${(2 s + 10)}^{\frac{1}{4}}$ .

${({(2 s + 10)}^{\frac{1}{4}})}^{4} = 4^{4}$

Simplify the left side.

Simplify ${({(2 s + 10)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(2 s + 10)}^{\frac{1}{4}})}^{4}$ .

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

${(2 s + 10)}^{\frac{1}{4} \cdot 4} = 4^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(2 s + 10)}^{\frac{1}{4} \cdot 4} = 4^{4}$

Rewrite the expression.

${(2 s + 10)}^{1} = 4^{4}$

Simplify.

$2 s + 10 = 4^{4}$

Simplify the right side.

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

$2 s + 10 = 256$

Step 3

Solve for $s$ .

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

Subtract $10$ from both sides of the equation.

$2 s = 256 - 10$

Subtract $10$ from $256$ .

$2 s = 246$

Divide each term in $2 s = 246$ by $2$ and simplify.

Divide each term in $2 s = 246$ by $2$ .

$\frac{2 s}{2} = \frac{246}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 s}{2} = \frac{246}{2}$

Divide $s$ by $1$ .

$s = \frac{246}{2}$

Simplify the right side.

Divide $246$ by $2$ .

$s = 123$