Basic Math Examples

$(a^{- 3} b^{4}) (a^{- 3} b^{- 6} c^{0})$

Step 1

Multiply $a^{- 3}$ by $a^{- 3}$ by adding the exponents.

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Step 1.1

Move $a^{- 3}$ .

$a^{- 3} a^{- 3} b^{4} (b^{- 6} c^{0})$

Step 1.2

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

$a^{- 3 - 3} b^{4} (b^{- 6} c^{0})$

Step 1.3

Subtract $3$ from $- 3$ .

$a^{- 6} b^{4} (b^{- 6} c^{0})$

Step 2

Simplify $a^{- 6} b^{4} (b^{- 6} c^{0})$ .

$a^{- 6} b^{4} b^{- 6}$

Step 3

Multiply $b^{4}$ by $b^{- 6}$ by adding the exponents.

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Step 3.1

Move $b^{- 6}$ .

$a^{- 6} (b^{- 6} b^{4})$

Step 3.2

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

$a^{- 6} b^{- 6 + 4}$

Step 3.3

Add $- 6$ and $4$ .

$a^{- 6} b^{- 2}$

Step 4

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

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

Step 5

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

$\frac{1}{a^{6}} \cdot \frac{1}{b^{2}}$

Step 6

Combine.

$\frac{1 \cdot 1}{a^{6} b^{2}}$

Step 7

Multiply $1$ by $1$ .

$\frac{1}{a^{6} b^{2}}$