Solve for d (2d+3)^(1/3)=2

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

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

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

Simplify the exponent.

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

${(2 d + 3)}^{1} = 2^{3}$

Simplify.

$2 d + 3 = 2^{3}$

Simplify the right side.

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

$2 d + 3 = 8$

Solve for $d$ .

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

Subtract $3$ from both sides of the equation.

$2 d = 8 - 3$

Subtract $3$ from $8$ .

$2 d = 5$

Divide each term in $2 d = 5$ by $2$ and simplify.

Divide each term in $2 d = 5$ by $2$ .

$\frac{2 d}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 d}{2} = \frac{5}{2}$

Divide $d$ by $1$ .

$d = \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$d = \frac{5}{2}$

Decimal Form:

$d = 2.5$

Mixed Number Form:

$d = 2 \frac{1}{2}$