Basic Math Examples

$(6 a b^{2}) {(12 a b^{- 2})}^{- 1}$

Step 1

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

$6 a b^{2} {(12 a \frac{1}{b^{2}})}^{- 1}$

Step 2

Multiply $12 a \frac{1}{b^{2}}$ .

Tap for more steps...

Step 2.1

Combine $12$ and $\frac{1}{b^{2}}$ .

$6 a b^{2} {(a \frac{12}{b^{2}})}^{- 1}$

Step 2.2

Combine $a$ and $\frac{12}{b^{2}}$ .

$6 a b^{2} {(\frac{a \cdot 12}{b^{2}})}^{- 1}$

Step 3

Move $12$ to the left of $a$ .

$6 a b^{2} {(\frac{12 \cdot a}{b^{2}})}^{- 1}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 5

Cancel the common factor of $6 a$ .

Tap for more steps...

Step 5.1

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

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

Step 5.2

Factor $6 a$ out of $12 a$ .

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

Step 5.3

Cancel the common factor.

$6 a b^{2} \frac{b^{2}}{6 a \cdot 2}$

Step 5.4

Rewrite the expression.

$b^{2} \frac{b^{2}}{2}$

Step 6

Combine $b^{2}$ and $\frac{b^{2}}{2}$ .

$\frac{b^{2} b^{2}}{2}$

Step 7

Multiply $b^{2}$ by $b^{2}$ by adding the exponents.

Tap for more steps...

Step 7.1

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

$\frac{b^{2 + 2}}{2}$

Step 7.2

Add $2$ and $2$ .

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