Solve for x fourth root of 6x+9+5=8

$\sqrt[4]{6 x + 9} + 5 = 8$

Step 1

Move all terms not containing $\sqrt[4]{6 x + 9}$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$\sqrt[4]{6 x + 9} = 8 - 5$

Subtract $5$ from $8$ .

$\sqrt[4]{6 x + 9} = 3$

Step 2

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

${\sqrt[4]{6 x + 9}}^{4} = 3^{4}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{6 x + 9}$ as ${(6 x + 9)}^{\frac{1}{4}}$ .

${({(6 x + 9)}^{\frac{1}{4}})}^{4} = 3^{4}$

Simplify the left side.

Simplify ${({(6 x + 9)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(6 x + 9)}^{\frac{1}{4}})}^{4}$ .

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

${(6 x + 9)}^{\frac{1}{4} \cdot 4} = 3^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(6 x + 9)}^{\frac{1}{4} \cdot 4} = 3^{4}$

Rewrite the expression.

${(6 x + 9)}^{1} = 3^{4}$

Simplify.

$6 x + 9 = 3^{4}$

Simplify the right side.

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

$6 x + 9 = 81$

Step 4

Solve for $x$ .

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

Subtract $9$ from both sides of the equation.

$6 x = 81 - 9$

Subtract $9$ from $81$ .

$6 x = 72$

Divide each term in $6 x = 72$ by $6$ and simplify.

Divide each term in $6 x = 72$ by $6$ .

$\frac{6 x}{6} = \frac{72}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{72}{6}$

Divide $x$ by $1$ .

$x = \frac{72}{6}$

Simplify the right side.

Divide $72$ by $6$ .

$x = 12$

Solve for x fourth root of 6x+9+5=8

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