Solve for t t^(2/3)=4

$t^{\frac{2}{3}} = 4$

Step 1

Raise each side of the equation to the power of $\frac{3}{2}$ to eliminate the fractional exponent on the left side.

${(t^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Step 2

Simplify the exponent.

Simplify the left side.

Simplify ${(t^{\frac{2}{3}})}^{\frac{3}{2}}$ .

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

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

$t^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$t^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Rewrite the expression.

$t^{\frac{1}{3} \cdot 3} = \pm 4^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$t^{\frac{1}{3} \cdot 3} = \pm 4^{\frac{3}{2}}$

Rewrite the expression.

$t^{1} = \pm 4^{\frac{3}{2}}$

Simplify.

$t = \pm 4^{\frac{3}{2}}$

Simplify the right side.

Simplify $\pm 4^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $4$ as $2^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$t = \pm 2^{3}$

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

$t = \pm 8$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$t = 8$

Next, use the negative value of the $\pm$ to find the second solution.

$t = - 8$

The complete solution is the result of both the positive and negative portions of the solution.

$t = 8, - 8$