Basic Math Examples

$\frac{3^{4} \cdot 2^{7}}{5^{2}} \div \frac{{(- 3)}^{2} \cdot 2^{6}}{5^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3^{4} \cdot 2^{7}}{5^{2}} \cdot \frac{5^{3}}{{(- 3)}^{2} \cdot 2^{6}}$

Step 2

Combine.

$\frac{3^{4} \cdot 2^{7} \cdot 5^{3}}{5^{2} ({(- 3)}^{2} \cdot 2^{6})}$

Step 3

Cancel the common factor of $2^{7}$ and $2^{6}$ .

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Step 3.1

Factor $2^{6}$ out of $3^{4} \cdot 2^{7} \cdot 5^{3}$ .

$\frac{2^{6} (3^{4} \cdot 2 \cdot 5^{3})}{5^{2} ({(- 3)}^{2} \cdot 2^{6})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2^{6}$ out of $5^{2} ({(- 3)}^{2} \cdot 2^{6})$ .

$\frac{2^{6} (3^{4} \cdot 2 \cdot 5^{3})}{2^{6} (5^{2} ({(- 3)}^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{2^{6} (3^{4} \cdot 2 \cdot 5^{3})}{2^{6} (5^{2} ({(- 3)}^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{3^{4} \cdot 2 \cdot 5^{3}}{5^{2} ({(- 3)}^{2})}$

Step 4

Cancel the common factor of $5^{3}$ and $5^{2}$ .

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Step 4.1

Factor $5^{2}$ out of $3^{4} \cdot 2 \cdot 5^{3}$ .

$\frac{5^{2} (3^{4} \cdot 2 \cdot 5)}{5^{2} ({(- 3)}^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Cancel the common factor.

$\frac{5^{2} (3^{4} \cdot 2 \cdot 5)}{5^{2} {(- 3)}^{2}}$

Step 4.2.2

Rewrite the expression.

$\frac{3^{4} \cdot 2 \cdot 5}{{(- 3)}^{2}}$

Step 5

Cancel the common factor of $3^{4}$ and ${(- 3)}^{2}$ .

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Step 5.1

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{{(- 1 (- 3))}^{4} \cdot 2 \cdot 5}{{(- 3)}^{2}}$

Step 5.2

Apply the product rule to $- 1 (- 3)$ .

$\frac{{(- 1)}^{4} {(- 3)}^{4} \cdot 2 \cdot 5}{{(- 3)}^{2}}$

Step 5.3

Raise $- 1$ to the power of $4$ .

$\frac{1 {(- 3)}^{4} \cdot 2 \cdot 5}{{(- 3)}^{2}}$

Step 5.4

Multiply ${(- 3)}^{4}$ by $1$ .

$\frac{{(- 3)}^{4} \cdot 2 \cdot 5}{{(- 3)}^{2}}$

Step 5.5

Factor ${(- 3)}^{2}$ out of ${(- 3)}^{4} \cdot 2 \cdot 5$ .

$\frac{{(- 3)}^{2} ({(- 3)}^{2} \cdot 2 \cdot 5)}{{(- 3)}^{2}}$

Step 5.6

Cancel the common factors.

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Step 5.6.1

Multiply by $1$ .

$\frac{{(- 3)}^{2} ({(- 3)}^{2} \cdot 2 \cdot 5)}{{(- 3)}^{2} \cdot 1}$

Step 5.6.2

Cancel the common factor.

$\frac{{(- 3)}^{2} ({(- 3)}^{2} \cdot 2 \cdot 5)}{{(- 3)}^{2} \cdot 1}$

Step 5.6.3

Rewrite the expression.

$\frac{{(- 3)}^{2} \cdot 2 \cdot 5}{1}$

Step 5.6.4

Divide ${(- 3)}^{2} \cdot 2 \cdot 5$ by $1$ .

${(- 3)}^{2} \cdot 2 \cdot 5$

Step 6

Raise $- 3$ to the power of $2$ .

$9 \cdot 2 \cdot 5$

Step 7

Multiply $9 \cdot 2 \cdot 5$ .

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Step 7.1

Multiply $9$ by $2$ .

$18 \cdot 5$

Step 7.2

Multiply $18$ by $5$ .

$90$