Basic Math Examples

${(\frac{2 c}{b})}^{3} \div \frac{8}{3 b c}$

Step 1

To divide by a fraction, multiply by its reciprocal.

${(\frac{2 c}{b})}^{3} \frac{3 b c}{8}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{2 c}{b}$ .

$\frac{{(2 c)}^{3}}{b^{3}} \cdot \frac{3 b c}{8}$

Step 2.2

Apply the product rule to $2 c$ .

$\frac{2^{3} c^{3}}{b^{3}} \cdot \frac{3 b c}{8}$

Step 3

Combine.

$\frac{2^{3} c^{3} (3 b c)}{b^{3} \cdot 8}$

Step 4

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

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Step 4.1

Move $c$ .

$\frac{2^{3} (c \cdot c^{3}) (3 b)}{b^{3} \cdot 8}$

Step 4.2

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

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Step 4.2.1

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

$\frac{2^{3} (c^{1} c^{3}) (3 b)}{b^{3} \cdot 8}$

Step 4.2.2

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

$\frac{2^{3} c^{1 + 3} (3 b)}{b^{3} \cdot 8}$

Step 4.3

Add $1$ and $3$ .

$\frac{2^{3} c^{4} (3 b)}{b^{3} \cdot 8}$

Step 5

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

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Step 5.1

Factor $b$ out of $2^{3} c^{4} (3 b)$ .

$\frac{b (2^{3} c^{4} \cdot (3))}{b^{3} \cdot 8}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $b$ out of $b^{3} \cdot 8$ .

$\frac{b (2^{3} c^{4} \cdot (3))}{b (b^{2} \cdot 8)}$

Step 5.2.2

Cancel the common factor.

$\frac{b (2^{3} c^{4} \cdot (3))}{b (b^{2} \cdot 8)}$

Step 5.2.3

Rewrite the expression.

$\frac{2^{3} c^{4} \cdot (3)}{b^{2} \cdot 8}$

Step 6

Simplify the numerator.

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Step 6.1

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

$\frac{8 c^{4} \cdot 3}{b^{2} \cdot 8}$

Step 6.2

Multiply $3$ by $8$ .

$\frac{24 c^{4}}{b^{2} \cdot 8}$

Step 7

Cancel the common factor of $24$ and $8$ .

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Step 7.1

Factor $8$ out of $24 c^{4}$ .

$\frac{8 (3 c^{4})}{b^{2} \cdot 8}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $8$ out of $b^{2} \cdot 8$ .

$\frac{8 (3 c^{4})}{8 \cdot b^{2}}$

Step 7.2.2

Cancel the common factor.

$\frac{8 (3 c^{4})}{8 \cdot b^{2}}$

Step 7.2.3

Rewrite the expression.

$\frac{3 c^{4}}{b^{2}}$