Algebra Examples

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

Step 1

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

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

Step 2

Move $x^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 3

Multiply $x^{\frac{4}{3}}$ by $x^{- \frac{2}{3}}$ by adding the exponents.

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Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $2$ from $4$ .

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

Step 4

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 0.\overline{6}$