Evaluate x^(4/3)=9

$x^{\frac{4}{3}} = 9$

Step 1

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

${(x^{\frac{4}{3}})}^{\frac{3}{4}} = \pm 9^{\frac{3}{4}}$

Step 2

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, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{4}{3} \cdot \frac{3}{4}} = \pm 9^{\frac{3}{4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$x^{\frac{4}{3} \cdot \frac{3}{4}} = \pm 9^{\frac{3}{4}}$

Rewrite the expression.

$x^{\frac{1}{3} \cdot 3} = \pm 9^{\frac{3}{4}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = \pm 9^{\frac{3}{4}}$

Rewrite the expression.

$x^{1} = \pm 9^{\frac{3}{4}}$

Simplify.

$x = \pm 9^{\frac{3}{4}}$

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.

$x = 9^{\frac{3}{4}}$

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

$x = - 9^{\frac{3}{4}}$

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

$x = 9^{\frac{3}{4}}, - 9^{\frac{3}{4}}$

Step 4

Exclude the solutions that do not make $x^{\frac{4}{3}} = 9$ true.

$x = 9^{\frac{3}{4}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 9^{\frac{3}{4}}$

Decimal Form:

$x = 5.19615242 \dots$