Solve for x fourth root of (2x+1)^3+2=3

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{{(2 x + 1)}^{3}}$ as ${(2 x + 1)}^{\frac{3}{4}}$ .

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

Step 2

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

Subtract $2$ from both sides of the equation.

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

Subtract $2$ from $3$ .

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

Step 3

Raise each side of the equation to the power of $\frac{4}{3}$ to eliminate the fractional exponent on the left side.

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

Step 4

Simplify the exponent.

Simplify the left side.

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

Multiply the exponents in ${({(2 x + 1)}^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$2 x + 1 = 1^{\frac{4}{3}}$

Simplify the right side.

One to any power is one.

$2 x + 1 = 1$

Step 5

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$2 x = 1 - 1$

Subtract $1$ from $1$ .

$2 x = 0$

Divide each term in $2 x = 0$ by $2$ and simplify.

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x = 0$

Solve for x fourth root of (2x+1)^3+2=3

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