Algebra Examples

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

Step 1

Move ${(c b^{- 3})}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Cancel the common factor of $4$ and $2$ .

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Step 2.1

Factor $2$ out of $4 c^{3} b^{4} {(c b^{- 3})}^{5}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.2.4

Divide $2 c^{3} b^{4} {(c b^{- 3})}^{5}$ by $1$ .

$2 c^{3} b^{4} {(c b^{- 3})}^{5}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 c^{3} b^{4} {(c \frac{1}{b^{3}})}^{5}$

Step 4

Combine $c$ and $\frac{1}{b^{3}}$ .

$2 c^{3} b^{4} {(\frac{c}{b^{3}})}^{5}$

Step 5

Apply basic rules of exponents.

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Step 5.1

Apply the product rule to $\frac{c}{b^{3}}$ .

$2 c^{3} b^{4} \frac{c^{5}}{{(b^{3})}^{5}}$

Step 5.2

Multiply the exponents in ${(b^{3})}^{5}$ .

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Step 5.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 c^{3} b^{4} \frac{c^{5}}{b^{3 \cdot 5}}$

Step 5.2.2

Multiply $3$ by $5$ .

$2 c^{3} b^{4} \frac{c^{5}}{b^{15}}$

Step 6

Cancel the common factor of $b^{4}$ .

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Step 6.1

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

$b^{4} (2 c^{3}) \frac{c^{5}}{b^{15}}$

Step 6.2

Factor $b^{4}$ out of $b^{15}$ .

$b^{4} (2 c^{3}) \frac{c^{5}}{b^{4} b^{11}}$

Step 6.3

Cancel the common factor.

$b^{4} (2 c^{3}) \frac{c^{5}}{b^{4} b^{11}}$

Step 6.4

Rewrite the expression.

$2 c^{3} \frac{c^{5}}{b^{11}}$

Step 7

Combine $2$ and $\frac{c^{5}}{b^{11}}$ .

$c^{3} \frac{2 c^{5}}{b^{11}}$

Step 8

Combine $c^{3}$ and $\frac{2 c^{5}}{b^{11}}$ .

$\frac{c^{3} (2 c^{5})}{b^{11}}$

Step 9

Multiply $c^{3}$ by $c^{5}$ by adding the exponents.

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Step 9.1

Move $c^{5}$ .

$\frac{c^{5} c^{3} \cdot 2}{b^{11}}$

Step 9.2

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

$\frac{c^{5 + 3} \cdot 2}{b^{11}}$

Step 9.3

Add $5$ and $3$ .

$\frac{c^{8} \cdot 2}{b^{11}}$

Step 10

Move $2$ to the left of $c^{8}$ .

$\frac{2 c^{8}}{b^{11}}$