Basic Math Examples

$(7 a b) {(- a^{4} b^{3})}^{2} {(2 a^{5} b^{6})}^{- 1}$

Step 1

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

Tap for more steps...

Step 1.1

Apply the product rule to $- a^{4} b^{3}$ .

$7 a b ({(- a^{4})}^{2} {(b^{3})}^{2}) {(2 a^{5} b^{6})}^{- 1}$

Step 1.2

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

$7 a b ({(- 1)}^{2} {(a^{4})}^{2} {(b^{3})}^{2}) {(2 a^{5} b^{6})}^{- 1}$

Step 2

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

$7 a b (1 {(a^{4})}^{2} {(b^{3})}^{2}) {(2 a^{5} b^{6})}^{- 1}$

Step 3

Multiply ${(a^{4})}^{2}$ by $1$ .

$7 a b ({(a^{4})}^{2} {(b^{3})}^{2}) {(2 a^{5} b^{6})}^{- 1}$

Step 4

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

Tap for more steps...

Step 4.1

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

$7 a b (a^{4 \cdot 2} {(b^{3})}^{2}) {(2 a^{5} b^{6})}^{- 1}$

Step 4.2

Multiply $4$ by $2$ .

$7 a b (a^{8} {(b^{3})}^{2}) {(2 a^{5} b^{6})}^{- 1}$

Step 5

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

Tap for more steps...

Step 5.1

Move $a^{8}$ .

$7 (a^{8} a) b {(b^{3})}^{2} {(2 a^{5} b^{6})}^{- 1}$

Step 5.2

Multiply $a^{8}$ by $a$ .

Tap for more steps...

Step 5.2.1

Raise $a$ to the power of $1$ .

$7 (a^{8} a^{1}) b {(b^{3})}^{2} {(2 a^{5} b^{6})}^{- 1}$

Step 5.2.2

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

$7 a^{8 + 1} b {(b^{3})}^{2} {(2 a^{5} b^{6})}^{- 1}$

Step 5.3

Add $8$ and $1$ .

$7 a^{9} b {(b^{3})}^{2} {(2 a^{5} b^{6})}^{- 1}$

Step 6

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

Tap for more steps...

Step 6.1

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

$7 a^{9} b \cdot b^{3 \cdot 2} {(2 a^{5} b^{6})}^{- 1}$

Step 6.2

Multiply $3$ by $2$ .

$7 a^{9} b \cdot b^{6} {(2 a^{5} b^{6})}^{- 1}$

Step 7

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

Tap for more steps...

Step 7.1

Move $b^{6}$ .

$7 a^{9} (b^{6} b) {(2 a^{5} b^{6})}^{- 1}$

Step 7.2

Multiply $b^{6}$ by $b$ .

Tap for more steps...

Step 7.2.1

Raise $b$ to the power of $1$ .

$7 a^{9} (b^{6} b^{1}) {(2 a^{5} b^{6})}^{- 1}$

Step 7.2.2

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

$7 a^{9} b^{6 + 1} {(2 a^{5} b^{6})}^{- 1}$

Step 7.3

Add $6$ and $1$ .

$7 a^{9} b^{7} {(2 a^{5} b^{6})}^{- 1}$

Step 8

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

$7 a^{9} b^{7} \frac{1}{2 a^{5} b^{6}}$

Step 9

Cancel the common factor of $a^{5} b^{6}$ .

Tap for more steps...

Step 9.1

Factor $a^{5} b^{6}$ out of $7 a^{9} b^{7}$ .

$a^{5} b^{6} (7 a^{4} b) \frac{1}{2 a^{5} b^{6}}$

Step 9.2

Factor $a^{5} b^{6}$ out of $2 a^{5} b^{6}$ .

$a^{5} b^{6} (7 a^{4} b) \frac{1}{a^{5} b^{6} (2)}$

Step 9.3

Cancel the common factor.

$a^{5} b^{6} (7 a^{4} b) \frac{1}{a^{5} b^{6} \cdot 2}$

Step 9.4

Rewrite the expression.

$7 a^{4} b \frac{1}{2}$

Step 10

Combine $7$ and $\frac{1}{2}$ .

$a^{4} b \frac{7}{2}$

Step 11

Combine $a^{4}$ and $\frac{7}{2}$ .

$b \frac{a^{4} \cdot 7}{2}$

Step 12

Combine $b$ and $\frac{a^{4} \cdot 7}{2}$ .

$\frac{b (a^{4} \cdot 7)}{2}$

Step 13

Move $7$ to the left of $b a^{4}$ .

$\frac{7 b a^{4}}{2}$