Algebra Examples

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

Step 1

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

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

Step 2

Raise $x$ to the power of $1$ .

$x^{a} = \frac{x^{\frac{4}{3}}}{x^{1}}$

Step 3

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

$x^{a} = x^{\frac{4}{3}} x^{- 1}$

Step 4

Multiply $x^{\frac{4}{3}}$ by $x^{- 1}$ by adding the exponents.

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Step 4.1

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

$x^{a} = x^{\frac{4}{3} - 1}$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{a} = x^{\frac{4}{3} - 1 \cdot \frac{3}{3}}$

Step 4.3

Combine $- 1$ and $\frac{3}{3}$ .

$x^{a} = x^{\frac{4}{3} + \frac{- 1 \cdot 3}{3}}$

Step 4.4

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{4 - 1 \cdot 3}{3}}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $3$ .

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

Step 4.5.2

Subtract $3$ from $4$ .

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

Step 5

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 0.\overline{3}$