Precalculus Examples

$\frac{6 a^{4} b^{- 5} c^{6}}{{(a^{- 2} b^{5} c)}^{4}}$

Step 1

Move $b^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{6 a^{4} c^{6}}{{(a^{- 2} b^{5} c)}^{4} b^{5}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $a^{- 2} b^{5} c$ .

$\frac{6 a^{4} c^{6}}{{(a^{- 2} b^{5})}^{4} c^{4} b^{5}}$

Step 2.2

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

$\frac{6 a^{4} c^{6}}{{(\frac{1}{a^{2}} b^{5})}^{4} c^{4} b^{5}}$

Step 2.3

Combine $\frac{1}{a^{2}}$ and $b^{5}$ .

$\frac{6 a^{4} c^{6}}{{(\frac{b^{5}}{a^{2}})}^{4} c^{4} b^{5}}$

Step 2.4

Apply the product rule to $\frac{b^{5}}{a^{2}}$ .

$\frac{6 a^{4} c^{6}}{\frac{{(b^{5})}^{4}}{{(a^{2})}^{4}} c^{4} b^{5}}$

Step 2.5

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

Tap for more steps...

Step 2.5.1

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

$\frac{6 a^{4} c^{6}}{\frac{b^{5 \cdot 4}}{{(a^{2})}^{4}} c^{4} b^{5}}$

Step 2.5.2

Multiply $5$ by $4$ .

$\frac{6 a^{4} c^{6}}{\frac{b^{20}}{{(a^{2})}^{4}} c^{4} b^{5}}$

Step 2.6

Multiply the exponents in ${(a^{2})}^{4}$ .

Tap for more steps...

Step 2.6.1

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

$\frac{6 a^{4} c^{6}}{\frac{b^{20}}{a^{2 \cdot 4}} c^{4} b^{5}}$

Step 2.6.2

Multiply $2$ by $4$ .

$\frac{6 a^{4} c^{6}}{\frac{b^{20}}{a^{8}} c^{4} b^{5}}$

Step 2.7

Combine exponents.

Tap for more steps...

Step 2.7.1

Combine $\frac{b^{20}}{a^{8}}$ and $c^{4}$ .

$\frac{6 a^{4} c^{6}}{\frac{b^{20} c^{4}}{a^{8}} b^{5}}$

Step 2.7.2

Combine $\frac{b^{20} c^{4}}{a^{8}}$ and $b^{5}$ .

$\frac{6 a^{4} c^{6}}{\frac{b^{20} c^{4} b^{5}}{a^{8}}}$

Step 2.7.3

Multiply $b^{20}$ by $b^{5}$ by adding the exponents.

Tap for more steps...

Step 2.7.3.1

Move $b^{5}$ .

$\frac{6 a^{4} c^{6}}{\frac{b^{5} b^{20} c^{4}}{a^{8}}}$

Step 2.7.3.2

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

$\frac{6 a^{4} c^{6}}{\frac{b^{5 + 20} c^{4}}{a^{8}}}$

Step 2.7.3.3

Add $5$ and $20$ .

$\frac{6 a^{4} c^{6}}{\frac{b^{25} c^{4}}{a^{8}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$6 a^{4} c^{6} \frac{a^{8}}{b^{25} c^{4}}$

Step 4

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

Tap for more steps...

Step 4.1

Factor $c^{4}$ out of $6 a^{4} c^{6}$ .

$c^{4} (6 a^{4} c^{2}) \frac{a^{8}}{b^{25} c^{4}}$

Step 4.2

Factor $c^{4}$ out of $b^{25} c^{4}$ .

$c^{4} (6 a^{4} c^{2}) \frac{a^{8}}{c^{4} b^{25}}$

Step 4.3

Cancel the common factor.

$c^{4} (6 a^{4} c^{2}) \frac{a^{8}}{c^{4} b^{25}}$

Step 4.4

Rewrite the expression.

$6 a^{4} c^{2} \frac{a^{8}}{b^{25}}$

Step 5

Combine $6$ and $\frac{a^{8}}{b^{25}}$ .

$a^{4} c^{2} \frac{6 a^{8}}{b^{25}}$

Step 6

Combine $a^{4}$ and $\frac{6 a^{8}}{b^{25}}$ .

$c^{2} \frac{a^{4} (6 a^{8})}{b^{25}}$

Step 7

Multiply $a^{4}$ by $a^{8}$ by adding the exponents.

Tap for more steps...

Step 7.1

Move $a^{8}$ .

$c^{2} \frac{a^{8} a^{4} \cdot 6}{b^{25}}$

Step 7.2

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

$c^{2} \frac{a^{8 + 4} \cdot 6}{b^{25}}$

Step 7.3

Add $8$ and $4$ .

$c^{2} \frac{a^{12} \cdot 6}{b^{25}}$

Step 8

Combine $c^{2}$ and $\frac{a^{12} \cdot 6}{b^{25}}$ .

$\frac{c^{2} (a^{12} \cdot 6)}{b^{25}}$

Step 9

Move $6$ to the left of $c^{2} a^{12}$ .

$\frac{6 c^{2} a^{12}}{b^{25}}$