Algebra Examples

$\frac{8 {(- m^{0} n^{2})}^{3} {(- n^{3})}^{2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Apply the product rule to $- m^{0} n^{2}$ .

$\frac{8 {(- m^{0})}^{3} {(n^{2})}^{3} {(- n^{3})}^{2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.2

Anything raised to $0$ is $1$ .

$\frac{8 {(- 1 \cdot 1)}^{3} {(n^{2})}^{3} {(- n^{3})}^{2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.3

Multiply $- 1$ by $1$ .

$\frac{8 {(- 1)}^{3} {(n^{2})}^{3} {(- n^{3})}^{2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.4

Raise $- 1$ to the power of $3$ .

$\frac{8 \cdot - 1 {(n^{2})}^{3} {(- n^{3})}^{2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.5

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

Tap for more steps...

Step 1.5.1

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

$\frac{8 \cdot - 1 n^{2 \cdot 3} {(- n^{3})}^{2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.5.2

Multiply $2$ by $3$ .

$\frac{8 \cdot - 1 n^{6} {(- n^{3})}^{2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.6

Apply the product rule to $- n^{3}$ .

$\frac{8 \cdot - 1 n^{6} ({(- 1)}^{2} {(n^{3})}^{2})}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.7

Raise $- 1$ to the power of $2$ .

$\frac{8 \cdot - 1 n^{6} (1 {(n^{3})}^{2})}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.8

Multiply ${(n^{3})}^{2}$ by $1$ .

$\frac{8 \cdot - 1 n^{6} {(n^{3})}^{2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.9

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

Tap for more steps...

Step 1.9.1

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

$\frac{8 \cdot - 1 n^{6} n^{3 \cdot 2}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.9.2

Multiply $3$ by $2$ .

$\frac{8 \cdot - 1 n^{6} n^{6}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.10

Combine exponents.

Tap for more steps...

Step 1.10.1

Factor out negative.

$\frac{- (8 n^{6} n^{6})}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.10.2

Multiply $n^{6}$ by $n^{6}$ by adding the exponents.

Tap for more steps...

Step 1.10.2.1

Move $n^{6}$ .

$\frac{- (8 (n^{6} n^{6}))}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.10.2.2

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

$\frac{- (8 n^{6 + 6})}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.10.2.3

Add $6$ and $6$ .

$\frac{- (8 n^{12})}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 1.10.3

Multiply $8$ by $- 1$ .

$\frac{- 8 n^{12}}{m^{6} n^{0} {(- 2 m^{- 2} n^{4})}^{3}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $- 2 m^{- 2} n^{4}$ .

$\frac{- 8 n^{12}}{m^{6} n^{0} {(- 2 m^{- 2})}^{3} {(n^{4})}^{3}}$

Step 2.2

Anything raised to $0$ is $1$ .

$\frac{- 8 n^{12}}{m^{6} \cdot 1 {(- 2 m^{- 2})}^{3} {(n^{4})}^{3}}$

Step 2.3

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

$\frac{- 8 n^{12}}{m^{6} \cdot 1 {(- 2 \frac{1}{m^{2}})}^{3} {(n^{4})}^{3}}$

Step 2.4

Combine $- 2$ and $\frac{1}{m^{2}}$ .

$\frac{- 8 n^{12}}{m^{6} \cdot 1 {(\frac{- 2}{m^{2}})}^{3} {(n^{4})}^{3}}$

Step 2.5

Move the negative in front of the fraction.

$\frac{- 8 n^{12}}{m^{6} \cdot 1 {(- \frac{2}{m^{2}})}^{3} {(n^{4})}^{3}}$

Step 2.6

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

Tap for more steps...

Step 2.6.1

Apply the product rule to $- \frac{2}{m^{2}}$ .

$\frac{- 8 n^{12}}{m^{6} \cdot 1 ({(- 1)}^{3} {(\frac{2}{m^{2}})}^{3}) {(n^{4})}^{3}}$

Step 2.6.2

Apply the product rule to $\frac{2}{m^{2}}$ .

$\frac{- 8 n^{12}}{m^{6} \cdot 1 ({(- 1)}^{3} \frac{2^{3}}{{(m^{2})}^{3}}) {(n^{4})}^{3}}$

Step 2.7

Raise $- 1$ to the power of $3$ .

$\frac{- 8 n^{12}}{m^{6} \cdot 1 (- \frac{2^{3}}{{(m^{2})}^{3}}) {(n^{4})}^{3}}$

Step 2.8

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

$\frac{- 8 n^{12}}{m^{6} \cdot 1 (- \frac{8}{{(m^{2})}^{3}}) {(n^{4})}^{3}}$

Step 2.9

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

Tap for more steps...

Step 2.9.1

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

$\frac{- 8 n^{12}}{m^{6} \cdot 1 (- \frac{8}{m^{2 \cdot 3}}) {(n^{4})}^{3}}$

Step 2.9.2

Multiply $2$ by $3$ .

$\frac{- 8 n^{12}}{m^{6} \cdot 1 (- \frac{8}{m^{6}}) {(n^{4})}^{3}}$

Step 2.10

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

Tap for more steps...

Step 2.10.1

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

$\frac{- 8 n^{12}}{m^{6} \cdot 1 (- \frac{8}{m^{6}}) n^{4 \cdot 3}}$

Step 2.10.2

Multiply $4$ by $3$ .

$\frac{- 8 n^{12}}{m^{6} \cdot 1 (- \frac{8}{m^{6}}) n^{12}}$

$\frac{- 8 n^{12}}{m^{6} \cdot 1 \cdot - 1 \frac{8}{m^{6}} n^{12}}$

Step 2.11

Combine exponents.

Tap for more steps...

Step 2.11.1

Factor out negative.

$\frac{- 8 n^{12}}{- (m^{6} \cdot 1 \frac{8}{m^{6}} n^{12})}$

Step 2.11.2

Multiply $m^{6}$ by $1$ .

$\frac{- 8 n^{12}}{- (m^{6} \frac{8}{m^{6}} n^{12})}$

Step 2.11.3

Combine $m^{6}$ and $\frac{8}{m^{6}}$ .

$\frac{- 8 n^{12}}{- (\frac{m^{6} \cdot 8}{m^{6}} n^{12})}$

Step 2.11.4

Combine $\frac{m^{6} \cdot 8}{m^{6}}$ and $n^{12}$ .

$\frac{- 8 n^{12}}{- \frac{m^{6} \cdot 8 n^{12}}{m^{6}}}$

Step 2.12

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 2.12.1

Reduce the expression $\frac{m^{6} \cdot 8 n^{12}}{m^{6}}$ by cancelling the common factors.

Tap for more steps...

Step 2.12.1.1

Cancel the common factor.

$\frac{- 8 n^{12}}{- \frac{m^{6} \cdot 8 n^{12}}{m^{6}}}$

Step 2.12.1.2

Rewrite the expression.

$\frac{- 8 n^{12}}{- \frac{8 n^{12}}{1}}$

Step 2.12.2

Divide $8 n^{12}$ by $1$ .

$\frac{- 8 n^{12}}{- (8 n^{12})}$

Step 3

Multiply $- 1$ by $8$ .

$\frac{- 8 n^{12}}{- 8 n^{12}}$

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Cancel the common factor of $- 8$ .

Tap for more steps...

Step 4.1.1

Cancel the common factor.

$\frac{- 8 n^{12}}{- 8 n^{12}}$

Step 4.1.2

Rewrite the expression.

$\frac{n^{12}}{n^{12}}$

Step 4.2

Cancel the common factor of $n^{12}$ .

Tap for more steps...

Step 4.2.1

Cancel the common factor.

$\frac{n^{12}}{n^{12}}$

Step 4.2.2

Rewrite the expression.

$1$