Solve for x 1/4 cube root of 2x+8=6

$\frac{1}{4} \sqrt[3]{2 x} + 8 = 6$

Move all terms not containing $\frac{1}{4} \cdot \sqrt[3]{2 x}$ to the right side of the equation.

Subtract $8$ from both sides of the equation.

$\frac{1}{4} \cdot \sqrt[3]{2 x} = 6 - 8$

Subtract $8$ from $6$ .

$\frac{1}{4} \cdot \sqrt[3]{2 x} = - 2$

To remove the radical on the left side of the equation, cube both sides of the equation.

${(\frac{1}{4} \cdot \sqrt[3]{2 x})}^{3} = {(- 2)}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x}$ as ${(2 x)}^{\frac{1}{3}}$ .

${(\frac{1}{4} \cdot {(2 x)}^{\frac{1}{3}})}^{3} = {(- 2)}^{3}$

Simplify the left side.

Simplify ${(\frac{1}{4} \cdot {(2 x)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $2 x$ .

${(\frac{1}{4} \cdot (2^{\frac{1}{3}} x^{\frac{1}{3}}))}^{3} = {(- 2)}^{3}$

Multiply $\frac{1}{4} (2^{\frac{1}{3}} x^{\frac{1}{3}})$ .

Combine $2^{\frac{1}{3}}$ and $\frac{1}{4}$ .

${(\frac{2^{\frac{1}{3}}}{4} x^{\frac{1}{3}})}^{3} = {(- 2)}^{3}$

Combine $\frac{2^{\frac{1}{3}}}{4}$ and $x^{\frac{1}{3}}$ .

${(\frac{2^{\frac{1}{3}} x^{\frac{1}{3}}}{4})}^{3} = {(- 2)}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2^{\frac{1}{3}} x^{\frac{1}{3}}}{4}$ .

$\frac{{(2^{\frac{1}{3}} x^{\frac{1}{3}})}^{3}}{4^{3}} = {(- 2)}^{3}$

Apply the product rule to $2^{\frac{1}{3}} x^{\frac{1}{3}}$ .

$\frac{{(2^{\frac{1}{3}})}^{3} {(x^{\frac{1}{3}})}^{3}}{4^{3}} = {(- 2)}^{3}$

Simplify the numerator.

Multiply the exponents in ${(2^{\frac{1}{3}})}^{3}$ .

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

$\frac{2^{\frac{1}{3} \cdot 3} {(x^{\frac{1}{3}})}^{3}}{4^{3}} = {(- 2)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2^{\frac{1}{3} \cdot 3} {(x^{\frac{1}{3}})}^{3}}{4^{3}} = {(- 2)}^{3}$

Rewrite the expression.

$\frac{2^{1} {(x^{\frac{1}{3}})}^{3}}{4^{3}} = {(- 2)}^{3}$

Evaluate the exponent.

$\frac{2 {(x^{\frac{1}{3}})}^{3}}{4^{3}} = {(- 2)}^{3}$

Multiply the exponents in ${(x^{\frac{1}{3}})}^{3}$ .

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

$\frac{2 x^{\frac{1}{3} \cdot 3}}{4^{3}} = {(- 2)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 x^{\frac{1}{3} \cdot 3}}{4^{3}} = {(- 2)}^{3}$

Rewrite the expression.

$\frac{2 x^{1}}{4^{3}} = {(- 2)}^{3}$

Simplify.

$\frac{2 x}{4^{3}} = {(- 2)}^{3}$

Reduce the expression by cancelling the common factors.

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

$\frac{2 x}{64} = {(- 2)}^{3}$

Cancel the common factor of $2$ and $64$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{64} = {(- 2)}^{3}$

Cancel the common factors.

Factor $2$ out of $64$ .

$\frac{2 x}{2 \cdot 32} = {(- 2)}^{3}$

Cancel the common factor.

$\frac{2 x}{2 \cdot 32} = {(- 2)}^{3}$

Rewrite the expression.

$\frac{x}{32} = {(- 2)}^{3}$

Simplify the right side.

Raise $- 2$ to the power of $3$ .

$\frac{x}{32} = - 8$

Solve for $x$ .

Multiply both sides of the equation by $32$ .

$32 \frac{x}{32} = 32 \cdot - 8$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $32$ .

Cancel the common factor.

$32 \frac{x}{32} = 32 \cdot - 8$

Rewrite the expression.

$x = 32 \cdot - 8$

Simplify the right side.

Multiply $32$ by $- 8$ .

$x = - 256$

Solve for x 1/4 cube root of 2x+8=6

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