Solve for x fourth root of 39-2x = fourth root of 2x-9

$\sqrt[4]{39 - 2 x} = \sqrt[4]{2 x - 9}$

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

${\sqrt[4]{39 - 2 x}}^{4} = {\sqrt[4]{2 x - 9}}^{4}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{39 - 2 x}$ as ${(39 - 2 x)}^{\frac{1}{4}}$ .

${({(39 - 2 x)}^{\frac{1}{4}})}^{4} = {\sqrt[4]{2 x - 9}}^{4}$

Simplify the left side.

Simplify ${({(39 - 2 x)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(39 - 2 x)}^{\frac{1}{4}})}^{4}$ .

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

${(39 - 2 x)}^{\frac{1}{4} \cdot 4} = {\sqrt[4]{2 x - 9}}^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(39 - 2 x)}^{\frac{1}{4} \cdot 4} = {\sqrt[4]{2 x - 9}}^{4}$

Rewrite the expression.

${(39 - 2 x)}^{1} = {\sqrt[4]{2 x - 9}}^{4}$

Simplify.

$39 - 2 x = {\sqrt[4]{2 x - 9}}^{4}$

Simplify the right side.

Rewrite ${\sqrt[4]{2 x - 9}}^{4}$ as $2 x - 9$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2 x - 9}$ as ${(2 x - 9)}^{\frac{1}{4}}$ .

$39 - 2 x = {({(2 x - 9)}^{\frac{1}{4}})}^{4}$

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

$39 - 2 x = {(2 x - 9)}^{\frac{1}{4} \cdot 4}$

Combine $\frac{1}{4}$ and $4$ .

$39 - 2 x = {(2 x - 9)}^{\frac{4}{4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$39 - 2 x = {(2 x - 9)}^{\frac{4}{4}}$

Rewrite the expression.

$39 - 2 x = {(2 x - 9)}^{1}$

Simplify.

$39 - 2 x = 2 x - 9$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$39 - 2 x - 2 x = - 9$

Subtract $2 x$ from $- 2 x$ .

$39 - 4 x = - 9$

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

Subtract $39$ from both sides of the equation.

$- 4 x = - 9 - 39$

Subtract $39$ from $- 9$ .

$- 4 x = - 48$

Divide each term in $- 4 x = - 48$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 48$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 48}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 48}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 48}{- 4}$

Simplify the right side.

Divide $- 48$ by $- 4$ .

$x = 12$

Solve for x fourth root of 39-2x = fourth root of 2x-9

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