Basic Math Examples

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

Step 1

Move ${(a^{- 5} b^{4})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $3 a^{5} b^{- 3}$ .

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

Step 2.2

Apply the product rule to $a^{- 5} b^{4}$ .

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

Step 2.3

Apply the product rule to $3 a^{5}$ .

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

Step 2.4

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

$\frac{1}{9 {(a^{5})}^{2} {(b^{- 3})}^{2} {(a^{- 5})}^{3} {(b^{4})}^{3}}$

Step 2.5

Multiply the exponents in ${(a^{5})}^{2}$ .

Tap for more steps...

Step 2.5.1

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

$\frac{1}{9 a^{5 \cdot 2} {(b^{- 3})}^{2} {(a^{- 5})}^{3} {(b^{4})}^{3}}$

Step 2.5.2

Multiply $5$ by $2$ .

$\frac{1}{9 a^{10} {(b^{- 3})}^{2} {(a^{- 5})}^{3} {(b^{4})}^{3}}$

Step 2.6

Multiply the exponents in ${(b^{- 3})}^{2}$ .

Tap for more steps...

Step 2.6.1

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

$\frac{1}{9 a^{10} b^{- 3 \cdot 2} {(a^{- 5})}^{3} {(b^{4})}^{3}}$

Step 2.6.2

Multiply $- 3$ by $2$ .

$\frac{1}{9 a^{10} b^{- 6} {(a^{- 5})}^{3} {(b^{4})}^{3}}$

Step 2.7

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

$\frac{1}{9 a^{10} \frac{1}{b^{6}} {(a^{- 5})}^{3} {(b^{4})}^{3}}$

Step 2.8

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

Tap for more steps...

Step 2.8.1

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

$\frac{1}{9 a^{10} \frac{1}{b^{6}} a^{- 5 \cdot 3} {(b^{4})}^{3}}$

Step 2.8.2

Multiply $- 5$ by $3$ .

$\frac{1}{9 a^{10} \frac{1}{b^{6}} a^{- 15} {(b^{4})}^{3}}$

Step 2.9

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

$\frac{1}{9 a^{10} \frac{1}{b^{6}} \frac{1}{a^{15}} {(b^{4})}^{3}}$

Step 2.10

Multiply the exponents in ${(b^{4})}^{3}$ .

Tap for more steps...

Step 2.10.1

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

$\frac{1}{9 a^{10} \frac{1}{b^{6}} \frac{1}{a^{15}} b^{4 \cdot 3}}$

Step 2.10.2

Multiply $4$ by $3$ .

$\frac{1}{9 a^{10} \frac{1}{b^{6}} \frac{1}{a^{15}} b^{12}}$

Step 2.11

Combine exponents.

Tap for more steps...

Step 2.11.1

Combine $9$ and $\frac{1}{b^{6}}$ .

$\frac{1}{a^{10} \frac{9}{b^{6}} \frac{1}{a^{15}} b^{12}}$

Step 2.11.2

Combine $a^{10}$ and $\frac{9}{b^{6}}$ .

$\frac{1}{\frac{a^{10} \cdot 9}{b^{6}} \cdot \frac{1}{a^{15}} b^{12}}$

Step 2.11.3

Multiply $\frac{a^{10} \cdot 9}{b^{6}}$ by $\frac{1}{a^{15}}$ .

$\frac{1}{\frac{a^{10} \cdot 9}{b^{6} a^{15}} b^{12}}$

Step 2.11.4

Combine $\frac{a^{10} \cdot 9}{b^{6} a^{15}}$ and $b^{12}$ .

$\frac{1}{\frac{a^{10} \cdot 9 b^{12}}{b^{6} a^{15}}}$

Step 2.12

Reduce the expression $\frac{a^{10} \cdot 9 b^{12}}{b^{6} a^{15}}$ by cancelling the common factors.

Tap for more steps...

Step 2.12.1

Factor $a^{10}$ out of $a^{10} \cdot 9 b^{12}$ .

$\frac{1}{\frac{a^{10} (9 b^{12})}{b^{6} a^{15}}}$

Step 2.12.2

Factor $a^{10}$ out of $b^{6} a^{15}$ .

$\frac{1}{\frac{a^{10} (9 b^{12})}{a^{10} (b^{6} a^{5})}}$

Step 2.12.3

Cancel the common factor.

$\frac{1}{\frac{a^{10} (9 b^{12})}{a^{10} (b^{6} a^{5})}}$

Step 2.12.4

Rewrite the expression.

$\frac{1}{\frac{9 b^{12}}{b^{6} a^{5}}}$

Step 2.13

Cancel the common factor of $b^{12}$ and $b^{6}$ .

Tap for more steps...

Step 2.13.1

Factor $b^{6}$ out of $9 b^{12}$ .

$\frac{1}{\frac{b^{6} (9 b^{6})}{b^{6} a^{5}}}$

Step 2.13.2

Cancel the common factors.

Tap for more steps...

Step 2.13.2.1

Factor $b^{6}$ out of $b^{6} a^{5}$ .

$\frac{1}{\frac{b^{6} (9 b^{6})}{b^{6} (a^{5})}}$

Step 2.13.2.2

Cancel the common factor.

$\frac{1}{\frac{b^{6} (9 b^{6})}{b^{6} a^{5}}}$

Step 2.13.2.3

Rewrite the expression.

$\frac{1}{\frac{9 b^{6}}{a^{5}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{a^{5}}{9 b^{6}}$

Step 4

Multiply $\frac{a^{5}}{9 b^{6}}$ by $1$ .

$\frac{a^{5}}{9 b^{6}}$