Solve for t (t-3)^(1/3)=2

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

Step 1

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

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

Step 2

Simplify the exponent.

Simplify the left side.

Simplify ${({(t - 3)}^{\frac{1}{3}})}^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

${(t - 3)}^{1} = 2^{3}$

Simplify.

$t - 3 = 2^{3}$

Simplify the right side.

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

$t - 3 = 8$

Step 3

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

Add $3$ to both sides of the equation.

$t = 8 + 3$

Add $8$ and $3$ .

$t = 11$