Solve the Rational Equation for x x^(4/3)=16

$x^{\frac{4}{3}} = 16$

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

${(x^{\frac{4}{3}})}^{\frac{3}{4}} = \pm 16^{\frac{3}{4}}$

Simplify the exponent.

Simplify the left side.

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

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

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

$x^{\frac{4}{3} \cdot \frac{3}{4}} = \pm 16^{\frac{3}{4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$x^{\frac{4}{3} \cdot \frac{3}{4}} = \pm 16^{\frac{3}{4}}$

Rewrite the expression.

$x^{\frac{1}{3} \cdot 3} = \pm 16^{\frac{3}{4}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = \pm 16^{\frac{3}{4}}$

Rewrite the expression.

$x^{1} = \pm 16^{\frac{3}{4}}$

Simplify.

$x = \pm 16^{\frac{3}{4}}$

Simplify the right side.

Simplify $\pm 16^{\frac{3}{4}}$ .

Simplify the expression.

Rewrite $16$ as $2^{4}$ .

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$x = \pm 2^{3}$

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

$x = \pm 8$

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.

$x = 8$

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

$x = - 8$

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

$x = 8, - 8$