Pre-Algebra Examples

${(\frac{a^{- 7} b}{a b^{8}})}^{- 2}$

Step 1

Move $a^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{b}{a b^{8} a^{7}})}^{- 2}$

Step 2

Multiply $a$ by $a^{7}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $a^{7}$ .

${(\frac{b}{a^{7} a b^{8}})}^{- 2}$

Step 2.2

Multiply $a^{7}$ by $a$ .

Tap for more steps...

Step 2.2.1

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

${(\frac{b}{a^{7} a^{1} b^{8}})}^{- 2}$

Step 2.2.2

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

${(\frac{b}{a^{7 + 1} b^{8}})}^{- 2}$

Step 2.3

Add $7$ and $1$ .

${(\frac{b}{a^{8} b^{8}})}^{- 2}$

Step 3

Cancel the common factor of $b$ and $b^{8}$ .

Tap for more steps...

Step 3.1

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

${(\frac{b^{1}}{a^{8} b^{8}})}^{- 2}$

Step 3.2

Factor $b$ out of $b^{1}$ .

${(\frac{b \cdot 1}{a^{8} b^{8}})}^{- 2}$

Step 3.3

Cancel the common factors.

Tap for more steps...

Step 3.3.1

Factor $b$ out of $a^{8} b^{8}$ .

${(\frac{b \cdot 1}{b (a^{8} b^{7})})}^{- 2}$

Step 3.3.2

Cancel the common factor.

${(\frac{b \cdot 1}{b (a^{8} b^{7})})}^{- 2}$

Step 3.3.3

Rewrite the expression.

${(\frac{1}{a^{8} b^{7}})}^{- 2}$

Step 4

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

${(a^{8} b^{7})}^{2}$

Step 5

Apply the product rule to $a^{8} b^{7}$ .

${(a^{8})}^{2} {(b^{7})}^{2}$

Step 6

Multiply the exponents in ${(a^{8})}^{2}$ .

Tap for more steps...

Step 6.1

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

$a^{8 \cdot 2} {(b^{7})}^{2}$

Step 6.2

Multiply $8$ by $2$ .

$a^{16} {(b^{7})}^{2}$

Step 7

Multiply the exponents in ${(b^{7})}^{2}$ .

Tap for more steps...

Step 7.1

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

$a^{16} b^{7 \cdot 2}$

Step 7.2

Multiply $7$ by $2$ .

$a^{16} b^{14}$