Pre-Algebra Examples

$\frac{\frac{\frac{72 m + 45}{8 m^{3}}}{32 m + 20}}{m}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{72 m + 45}{8 m^{3}}}{32 m + 20} \cdot \frac{1}{m}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{72 m + 45}{8 m^{3}} \cdot \frac{1}{32 m + 20} \frac{1}{m}$

Step 3

Factor $9$ out of $72 m + 45$ .

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Step 3.1

Factor $9$ out of $72 m$ .

$\frac{9 (8 m) + 45}{8 m^{3}} \cdot \frac{1}{32 m + 20} \frac{1}{m}$

Step 3.2

Factor $9$ out of $45$ .

$\frac{9 (8 m) + 9 (5)}{8 m^{3}} \cdot \frac{1}{32 m + 20} \frac{1}{m}$

Step 3.3

Factor $9$ out of $9 (8 m) + 9 (5)$ .

$\frac{9 (8 m + 5)}{8 m^{3}} \cdot \frac{1}{32 m + 20} \frac{1}{m}$

Step 4

Factor $4$ out of $32 m + 20$ .

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Step 4.1

Factor $4$ out of $32 m$ .

$\frac{9 (8 m + 5)}{8 m^{3}} \cdot \frac{1}{4 (8 m) + 20} \frac{1}{m}$

Step 4.2

Factor $4$ out of $20$ .

$\frac{9 (8 m + 5)}{8 m^{3}} \cdot \frac{1}{4 (8 m) + 4 (5)} \frac{1}{m}$

Step 4.3

Factor $4$ out of $4 (8 m) + 4 (5)$ .

$\frac{9 (8 m + 5)}{8 m^{3}} \cdot \frac{1}{4 (8 m + 5)} \frac{1}{m}$

Step 5

Combine.

$\frac{9 (8 m + 5) \cdot 1}{8 m^{3} (4 (8 m + 5))} \cdot \frac{1}{m}$

Step 6

Combine.

$\frac{9 (8 m + 5) \cdot 1 \cdot 1}{8 m^{3} (4 (8 m + 5)) m}$

Step 7

Multiply $m^{3}$ by $m$ by adding the exponents.

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Step 7.1

Move $m$ .

$\frac{9 (8 m + 5) \cdot 1 \cdot 1}{8 (m \cdot m^{3}) (4 (8 m + 5))}$

Step 7.2

Multiply $m$ by $m^{3}$ .

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Step 7.2.1

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

$\frac{9 (8 m + 5) \cdot 1 \cdot 1}{8 (m^{1} m^{3}) (4 (8 m + 5))}$

Step 7.2.2

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

$\frac{9 (8 m + 5) \cdot 1 \cdot 1}{8 m^{1 + 3} (4 (8 m + 5))}$

Step 7.3

Add $1$ and $3$ .

$\frac{9 (8 m + 5) \cdot 1 \cdot 1}{8 m^{4} (4 (8 m + 5))}$

Step 8

Multiply $9 (8 m + 5)$ by $1$ .

$\frac{9 (8 m + 5) \cdot 1}{8 m^{4} (4 (8 m + 5))}$

Step 9

Multiply $9 (8 m + 5)$ by $1$ .

$\frac{9 (8 m + 5)}{8 m^{4} (4 (8 m + 5))}$

Step 10

Cancel the common factor of $8 m + 5$ .

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Step 10.1

Cancel the common factor.

$\frac{9 (8 m + 5)}{8 m^{4} (4 (8 m + 5))}$

Step 10.2

Rewrite the expression.

$\frac{9}{8 m^{4} \cdot (4)}$

Step 11

Multiply $4$ by $8$ .

$\frac{9}{32 m^{4}}$