Finite Math Examples

$(4 x^{2} y) (- 5 x y^{- 3})$

Step 1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.1

Move $x$ .

$4 (x \cdot x^{2}) y (- 5 y^{- 3})$

Step 1.2

Multiply $x$ by $x^{2}$ .

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Step 1.2.1

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

$4 (x^{1} x^{2}) y (- 5 y^{- 3})$

Step 1.2.2

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

$4 x^{1 + 2} y (- 5 y^{- 3})$

Step 1.3

Add $1$ and $2$ .

$4 x^{3} y (- 5 y^{- 3})$

Step 2

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

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Step 2.1

Move $y^{- 3}$ .

$4 x^{3} (y^{- 3} y) \cdot - 5$

Step 2.2

Multiply $y^{- 3}$ by $y$ .

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Step 2.2.1

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

$4 x^{3} (y^{- 3} y^{1}) \cdot - 5$

Step 2.2.2

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

$4 x^{3} y^{- 3 + 1} \cdot - 5$

Step 2.3

Add $- 3$ and $1$ .

$4 x^{3} y^{- 2} \cdot - 5$

Step 3

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

$4 x^{3} \frac{1}{y^{2}} \cdot - 5$

Step 4

Multiply $4 x^{3} \frac{1}{y^{2}}$ .

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Step 4.1

Combine $4$ and $\frac{1}{y^{2}}$ .

$x^{3} \frac{4}{y^{2}} \cdot - 5$

Step 4.2

Combine $x^{3}$ and $\frac{4}{y^{2}}$ .

$\frac{x^{3} \cdot 4}{y^{2}} \cdot - 5$

Step 5

Move $4$ to the left of $x^{3}$ .

$\frac{4 \cdot x^{3}}{y^{2}} \cdot - 5$

Step 6

Multiply $\frac{4 x^{3}}{y^{2}} \cdot - 5$ .

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Step 6.1

Combine $\frac{4 x^{3}}{y^{2}}$ and $- 5$ .

$\frac{4 x^{3} \cdot - 5}{y^{2}}$

Step 6.2

Multiply $- 5$ by $4$ .

$\frac{- 20 x^{3}}{y^{2}}$

Step 7

Move the negative in front of the fraction.

$- \frac{20 x^{3}}{y^{2}}$