Basic Math Examples

$a^{- 2 b} \div a^{b + 1}$

Step 1

Rewrite the division as a fraction.

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

Step 2

Cancel the common factor of $a^{- 2 b}$ and $a^{b + 1}$ .

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Step 2.1

Factor $a^{b + 1}$ out of $a^{- 2 b}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.2.4

Divide $a^{- 2 b - (b + 1)}$ by $1$ .

$a^{- 2 b - (b + 1)}$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $- 1$ by $1$ .

$a^{- 2 b - b - 1}$

Step 4

Subtract $b$ from $- 2 b$ .

$a^{- 3 b - 1}$