Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply $\frac{2}{3} \cdot 2$ .

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Step 4.1

Combine $\frac{2}{3}$ and $2$ .

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

Step 4.2

Multiply $2$ by $2$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 1.\overline{3}$

Mixed Number Form:

$a = 1 \frac{1}{3}$