Basic Math Examples

$\frac{8 s}{3} \cdot \frac{6 a^{3}}{s^{3}} \div \frac{s^{2}}{6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 s}{3} \cdot \frac{6 a^{3}}{s^{3}} \frac{6}{s^{2}}$

Step 2

Combine.

$\frac{8 s (6 a^{3})}{3 s^{3}} \cdot \frac{6}{s^{2}}$

Step 3

Combine.

$\frac{8 s (6 a^{3}) \cdot 6}{3 s^{3} s^{2}}$

Step 4

Multiply $s^{3}$ by $s^{2}$ by adding the exponents.

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Step 4.1

Move $s^{2}$ .

$\frac{8 s (6 a^{3}) \cdot 6}{3 (s^{2} s^{3})}$

Step 4.2

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

$\frac{8 s (6 a^{3}) \cdot 6}{3 s^{2 + 3}}$

Step 4.3

Add $2$ and $3$ .

$\frac{8 s (6 a^{3}) \cdot 6}{3 s^{5}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

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

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Step 5.1.1

Factor $s$ out of $8 s (6 a^{3}) \cdot 6$ .

$\frac{s ((8 (6 a^{3})) \cdot 6)}{3 s^{5}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $s$ out of $3 s^{5}$ .

$\frac{s ((8 (6 a^{3})) \cdot 6)}{s (3 s^{4})}$

Step 5.1.2.2

Cancel the common factor.

$\frac{s ((8 (6 a^{3})) \cdot 6)}{s (3 s^{4})}$

Step 5.1.2.3

Rewrite the expression.

$\frac{(8 (6 a^{3})) \cdot 6}{3 s^{4}}$

Step 5.2

Cancel the common factor of $6$ and $3$ .

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Step 5.2.1

Factor $3$ out of $(8 (6 a^{3})) \cdot 6$ .

$\frac{3 (8 (2 a^{3}) \cdot 6)}{3 s^{4}}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $3$ out of $3 s^{4}$ .

$\frac{3 (8 (2 a^{3}) \cdot 6)}{3 (s^{4})}$

Step 5.2.2.2

Cancel the common factor.

$\frac{3 (8 (2 a^{3}) \cdot 6)}{3 s^{4}}$

Step 5.2.2.3

Rewrite the expression.

$\frac{8 (2 a^{3}) \cdot 6}{s^{4}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $8$ by $2$ .

$\frac{16 a^{3} \cdot 6}{s^{4}}$

Step 6.2

Multiply $6$ by $16$ .

$\frac{96 a^{3}}{s^{4}}$