Solve for a (x^(4/3))^(3/2)=x^a

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

Step 1

Rewrite the equation as $x^{a} = {(x^{\frac{4}{3}})}^{\frac{3}{2}}$ .

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

Step 2

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

$x^{a} = x^{\frac{4}{3} \cdot \frac{3}{2}}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$a = \frac{4}{3} \cdot \frac{3}{2}$

Step 4

Simplify $\frac{4}{3} \cdot \frac{3}{2}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$a = \frac{2 (2)}{3} \cdot \frac{3}{2}$

Cancel the common factor.

$a = \frac{2 \cdot 2}{3} \cdot \frac{3}{2}$

Rewrite the expression.

$a = \frac{2}{3} \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$a = \frac{2}{3} \cdot 3$

Rewrite the expression.

$a = 2$