Solve for x -7+(2x+3)^(1/3)=0

$- 7 + {(2 x + 3)}^{\frac{1}{3}} = 0$

Step 1

Add $7$ to both sides of the equation.

${(2 x + 3)}^{\frac{1}{3}} = 7$

Step 2

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${({(2 x + 3)}^{\frac{1}{3}})}^{3} = 7^{3}$

Step 3

Simplify the exponent.

Simplify the left side.

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

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

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

${(2 x + 3)}^{\frac{1}{3} \cdot 3} = 7^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x + 3)}^{\frac{1}{3} \cdot 3} = 7^{3}$

Rewrite the expression.

${(2 x + 3)}^{1} = 7^{3}$

Simplify.

$2 x + 3 = 7^{3}$

Simplify the right side.

Raise $7$ to the power of $3$ .

$2 x + 3 = 343$

Step 4

Solve for $x$ .

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

Subtract $3$ from both sides of the equation.

$2 x = 343 - 3$

Subtract $3$ from $343$ .

$2 x = 340$

Divide each term in $2 x = 340$ by $2$ and simplify.

Divide each term in $2 x = 340$ by $2$ .

$\frac{2 x}{2} = \frac{340}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{340}{2}$

Divide $x$ by $1$ .

$x = \frac{340}{2}$

Simplify the right side.

Divide $340$ by $2$ .

$x = 170$