Basic Math Examples

$(a^{- 6} b^{- 5}) (a^{- 5} b^{- 8})$

Step 1

Multiply $a^{- 6}$ by $a^{- 5}$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $a^{- 5}$ .

$a^{- 5} a^{- 6} b^{- 5} b^{- 8}$

Step 1.2

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

$a^{- 5 - 6} b^{- 5} b^{- 8}$

Step 1.3

Subtract $6$ from $- 5$ .

$a^{- 11} b^{- 5} b^{- 8}$

Step 2

Multiply $b^{- 5}$ by $b^{- 8}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $b^{- 8}$ .

$a^{- 11} (b^{- 8} b^{- 5})$

Step 2.2

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

$a^{- 11} b^{- 8 - 5}$

Step 2.3

Subtract $5$ from $- 8$ .

$a^{- 11} b^{- 13}$

Step 3

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

$\frac{1}{a^{11}} b^{- 13}$

Step 4

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

$\frac{1}{a^{11}} \cdot \frac{1}{b^{13}}$

Step 5

Combine.

$\frac{1 \cdot 1}{a^{11} b^{13}}$

Step 6

Multiply $1$ by $1$ .

$\frac{1}{a^{11} b^{13}}$