Basic Math Examples

$\frac{a^{3} b^{\frac{- 1}{2}}}{a b^{\frac{- 3}{2}}}$

Step 1

Move $b^{\frac{- 3}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{3} b^{\frac{- 1}{2}} b^{- \frac{- 3}{2}}}{a}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $b^{\frac{- 1}{2}}$ by $b^{- \frac{- 3}{2}}$ by adding the exponents.

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Step 2.1.1

Move $b^{- \frac{- 3}{2}}$ .

$\frac{a^{3} (b^{- \frac{- 3}{2}} b^{\frac{- 1}{2}})}{a}$

Step 2.1.2

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

$\frac{a^{3} b^{- \frac{- 3}{2} + \frac{- 1}{2}}}{a}$

Step 2.1.3

Combine the numerators over the common denominator.

$\frac{a^{3} b^{\frac{3 - 1}{2}}}{a}$

Step 2.1.4

Subtract $1$ from $3$ .

$\frac{a^{3} b^{\frac{2}{2}}}{a}$

Step 2.1.5

Divide $2$ by $2$ .

$\frac{a^{3} b^{1}}{a}$

Step 2.2

Simplify $a^{3} b^{1}$ .

$\frac{a^{3} b}{a}$

Step 3

Cancel the common factor of $a^{3}$ and $a$ .

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Step 3.1

Factor $a$ out of $a^{3} b$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.2.5

Divide $a^{2} b$ by $1$ .

$a^{2} b$