Basic Math Examples

$a^{- 7} \cdot b^{3} \cdot a^{5} \cdot b^{- 5}$

Step 1

Multiply $a^{- 7}$ by $a^{5}$ by adding the exponents.

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Step 1.1

Move $a^{5}$ .

$a^{5} a^{- 7} \cdot b^{3} \cdot b^{- 5}$

Step 1.2

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

$a^{5 - 7} \cdot b^{3} \cdot b^{- 5}$

Step 1.3

Subtract $7$ from $5$ .

$a^{- 2} \cdot b^{3} \cdot b^{- 5}$

Step 2

Multiply $b^{3}$ by $b^{- 5}$ by adding the exponents.

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Step 2.1

Move $b^{- 5}$ .

$a^{- 2} \cdot (b^{- 5} b^{3})$

Step 2.2

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

$a^{- 2} \cdot b^{- 5 + 3}$

Step 2.3

Add $- 5$ and $3$ .

$a^{- 2} \cdot b^{- 2}$

Step 3

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

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

Step 4

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

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

Step 5

Combine.

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

Step 6

Multiply $1$ by $1$ .

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