Algebra Examples

$\frac{8^{\frac{2}{3}}}{8^{\frac{1}{3}}}$

Step 1

Move $8^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$8^{\frac{2}{3}} \cdot 8^{- \frac{1}{3}}$

Step 2

Multiply $8^{\frac{2}{3}}$ by $8^{- \frac{1}{3}}$ by adding the exponents.

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Step 2.1

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

$8^{\frac{2}{3} - \frac{1}{3}}$

Step 2.2

Combine the numerators over the common denominator.

$8^{\frac{2 - 1}{3}}$

Step 2.3

Subtract $1$ from $2$ .

$8^{\frac{1}{3}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[3]{8^{1}}$

Step 4

Anything raised to $1$ is the base itself.

$\sqrt[3]{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{8}$

Decimal Form:

$2$