Finite Math Examples

$- \frac{5 m^{2}}{8} \cdot \sqrt[5]{m^{2}}$

Step 1

Combine $\sqrt[5]{m^{2}}$ and $\frac{5 m^{2}}{8}$ .

$- \frac{\sqrt[5]{m^{2}} (5 m^{2})}{8}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{m^{2}}$ as $m^{\frac{2}{5}}$ .

$- \frac{5 (m^{\frac{2}{5}} m^{2})}{8}$

Step 3

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

$- \frac{5 m^{\frac{2}{5} + 2}}{8}$

Step 4

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{5 m^{\frac{2}{5} + 2 \cdot \frac{5}{5}}}{8}$

Step 5

Combine $2$ and $\frac{5}{5}$ .

$- \frac{5 m^{\frac{2}{5} + \frac{2 \cdot 5}{5}}}{8}$

Step 6

Combine the numerators over the common denominator.

$- \frac{5 m^{\frac{2 + 2 \cdot 5}{5}}}{8}$

Step 7

Simplify the numerator.

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Multiply $2$ by $5$ .

$- \frac{5 m^{\frac{2 + 10}{5}}}{8}$

Add $2$ and $10$ .

$- \frac{5 m^{\frac{12}{5}}}{8}$