Basic Math Examples

$2 \sqrt[4]{\frac{m^{11}}{81}} - 3 m^{2} \sqrt[4]{\frac{m^{3}}{16}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\frac{m^{11}}{81}$ as ${(\frac{m^{2}}{3})}^{4} m^{3}$ .

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Step 1.1.1

Factor the perfect power ${(m^{2})}^{4}$ out of $m^{11}$ .

$2 \sqrt[4]{\frac{{(m^{2})}^{4} m^{3}}{81}} - 3 m^{2} \sqrt[4]{\frac{m^{3}}{16}}$

Step 1.1.2

Factor the perfect power $3^{4}$ out of $81$ .

$2 \sqrt[4]{\frac{{(m^{2})}^{4} m^{3}}{3^{4} \cdot 1}} - 3 m^{2} \sqrt[4]{\frac{m^{3}}{16}}$

Step 1.1.3

Rearrange the fraction $\frac{{(m^{2})}^{4} m^{3}}{3^{4} \cdot 1}$ .

$2 \sqrt[4]{{(\frac{m^{2}}{3})}^{4} m^{3}} - 3 m^{2} \sqrt[4]{\frac{m^{3}}{16}}$

Step 1.2

Pull terms out from under the radical.

$2 (\frac{m^{2}}{3} \sqrt[4]{m^{3}}) - 3 m^{2} \sqrt[4]{\frac{m^{3}}{16}}$

Step 1.3

Combine $\frac{m^{2}}{3}$ and $\sqrt[4]{m^{3}}$ .

$2 \frac{m^{2} \sqrt[4]{m^{3}}}{3} - 3 m^{2} \sqrt[4]{\frac{m^{3}}{16}}$

Step 1.4

Combine $2$ and $\frac{m^{2} \sqrt[4]{m^{3}}}{3}$ .

$\frac{2 (m^{2} \sqrt[4]{m^{3}})}{3} - 3 m^{2} \sqrt[4]{\frac{m^{3}}{16}}$

Step 1.5

Rewrite $\frac{m^{3}}{16}$ as ${(\frac{1}{2})}^{4} m^{3}$ .

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Step 1.5.1

Factor the perfect power $1^{4}$ out of $m^{3}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} - 3 m^{2} \sqrt[4]{\frac{1^{4} m^{3}}{16}}$

Step 1.5.2

Factor the perfect power $2^{4}$ out of $16$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} - 3 m^{2} \sqrt[4]{\frac{1^{4} m^{3}}{2^{4} \cdot 1}}$

Step 1.5.3

Rearrange the fraction $\frac{1^{4} m^{3}}{2^{4} \cdot 1}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} - 3 m^{2} \sqrt[4]{{(\frac{1}{2})}^{4} m^{3}}$

Step 1.6

Pull terms out from under the radical.

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} - 3 m^{2} (\frac{1}{2} \sqrt[4]{m^{3}})$

Step 1.7

Combine $\frac{1}{2}$ and $\sqrt[4]{m^{3}}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} - 3 m^{2} \frac{\sqrt[4]{m^{3}}}{2}$

Step 1.8

Multiply $- 3 m^{2} \frac{\sqrt[4]{m^{3}}}{2}$ .

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Step 1.8.1

Combine $- 3$ and $\frac{\sqrt[4]{m^{3}}}{2}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} + m^{2} \frac{- 3 \sqrt[4]{m^{3}}}{2}$

Step 1.8.2

Combine $m^{2}$ and $\frac{- 3 \sqrt[4]{m^{3}}}{2}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} + \frac{m^{2} (- 3 \sqrt[4]{m^{3}})}{2}$

Step 1.9

Remove unnecessary parentheses.

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} + \frac{m^{2} \cdot - 3 \sqrt[4]{m^{3}}}{2}$

Step 1.10

Move $- 3$ to the left of $m^{2}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} + \frac{- 3 \cdot m^{2} \sqrt[4]{m^{3}}}{2}$

Step 1.11

Move the negative in front of the fraction.

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} - \frac{3 m^{2} \sqrt[4]{m^{3}}}{2}$

Step 2

To write $\frac{2 m^{2} \sqrt[4]{m^{3}}}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} \cdot \frac{2}{2} - \frac{3 m^{2} \sqrt[4]{m^{3}}}{2}$

Step 3

To write $- \frac{3 m^{2} \sqrt[4]{m^{3}}}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}}}{3} \cdot \frac{2}{2} - \frac{3 m^{2} \sqrt[4]{m^{3}}}{2} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2 m^{2} \sqrt[4]{m^{3}}}{3}$ by $\frac{2}{2}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}} \cdot 2}{3 \cdot 2} - \frac{3 m^{2} \sqrt[4]{m^{3}}}{2} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}} \cdot 2}{6} - \frac{3 m^{2} \sqrt[4]{m^{3}}}{2} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{3 m^{2} \sqrt[4]{m^{3}}}{2}$ by $\frac{3}{3}$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}} \cdot 2}{6} - \frac{3 m^{2} \sqrt[4]{m^{3}} \cdot 3}{2 \cdot 3}$

Step 4.4

Multiply $2$ by $3$ .

$\frac{2 m^{2} \sqrt[4]{m^{3}} \cdot 2}{6} - \frac{3 m^{2} \sqrt[4]{m^{3}} \cdot 3}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 m^{2} \sqrt[4]{m^{3}} \cdot 2 - 3 m^{2} \sqrt[4]{m^{3}} \cdot 3}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $m^{2} \sqrt[4]{m^{3}}$ out of $2 m^{2} \sqrt[4]{m^{3}} \cdot 2 - 3 m^{2} \sqrt[4]{m^{3}} \cdot 3$ .

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Step 6.1.1

Factor $m^{2} \sqrt[4]{m^{3}}$ out of $2 m^{2} \sqrt[4]{m^{3}} \cdot 2$ .

$\frac{m^{2} \sqrt[4]{m^{3}} (2 \cdot 2) - 3 m^{2} \sqrt[4]{m^{3}} \cdot 3}{6}$

Step 6.1.2

Factor $m^{2} \sqrt[4]{m^{3}}$ out of $- 3 m^{2} \sqrt[4]{m^{3}} \cdot 3$ .

$\frac{m^{2} \sqrt[4]{m^{3}} (2 \cdot 2) + m^{2} \sqrt[4]{m^{3}} (- 3 \cdot 3)}{6}$

Step 6.1.3

Factor $m^{2} \sqrt[4]{m^{3}}$ out of $m^{2} \sqrt[4]{m^{3}} (2 \cdot 2) + m^{2} \sqrt[4]{m^{3}} (- 3 \cdot 3)$ .

$\frac{m^{2} \sqrt[4]{m^{3}} (2 \cdot 2 - 3 \cdot 3)}{6}$

Step 6.2

Combine exponents.

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Step 6.2.1

Multiply $2$ by $2$ .

$\frac{m^{2} \sqrt[4]{m^{3}} (4 - 3 \cdot 3)}{6}$

Step 6.2.2

Multiply $- 3$ by $3$ .

$\frac{m^{2} \sqrt[4]{m^{3}} (4 - 9)}{6}$

Step 6.3

Subtract $9$ from $4$ .

$\frac{m^{2} \sqrt[4]{m^{3}} \cdot - 5}{6}$

Step 7

Simplify the expression.

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Step 7.1

Move $- 5$ to the left of $m^{2} \sqrt[4]{m^{3}}$ .

$\frac{- 5 \cdot (m^{2} \sqrt[4]{m^{3}})}{6}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{5 m^{2} \sqrt[4]{m^{3}}}{6}$