Algebra Examples

$\frac{12 a^{5}}{- 4 {(a^{5})}^{4}}$

Step 1

Cancel the common factor of $12$ and $- 4$ .

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Step 1.1

Factor $4$ out of $12 a^{5}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $- 4 {(a^{5})}^{4}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Multiply the exponents in ${(a^{5})}^{4}$ .

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Step 2.1

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

$\frac{3 a^{5}}{- a^{5 \cdot 4}}$

Step 2.2

Multiply $5$ by $4$ .

$\frac{3 a^{5}}{- a^{20}}$

Step 3

Cancel the common factor of $a^{5}$ and $a^{20}$ .

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Step 3.1

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

$\frac{a^{5} \cdot 3}{- a^{20}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a^{5}$ out of $- a^{20}$ .

$\frac{a^{5} \cdot 3}{a^{5} (- a^{15})}$

Step 3.2.2

Cancel the common factor.

$\frac{a^{5} \cdot 3}{a^{5} (- a^{15})}$

Step 3.2.3

Rewrite the expression.

$\frac{3}{- a^{15}}$

Step 4

Move the negative in front of the fraction.

$- \frac{3}{a^{15}}$