Basic Math Examples

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

Step 1

Combine.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

Combine fractions.

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Step 4.1

Multiply $\frac{1}{b^{2}}$ by $\frac{1}{a}$ .

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

Step 4.2

Multiply $\frac{1}{b^{3}}$ by $\frac{1}{a^{2}}$ .

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

Step 5

Multiply the numerator by the reciprocal of the denominator.

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

Step 6

Cancel the common factor of $b^{2} a$ .

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Step 6.1

Factor $b^{2} a$ out of $b^{3} a^{2}$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

$b a \cdot \frac{t}{t - 1}$

Step 7

Multiply $b a \frac{t}{t - 1}$ .

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Step 7.1

Combine $b$ and $\frac{t}{t - 1}$ .

$a \frac{b t}{t - 1}$

Step 7.2

Combine $a$ and $\frac{b t}{t - 1}$ .

$\frac{a (b t)}{t - 1}$

$\frac{a b t}{t - 1}$