Algebra Examples

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

Step 1

Multiply $x^{2}$ by $x^{- 5}$ by adding the exponents.

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Step 1.1

Move $x^{- 5}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 5$ and $2$ .

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

Step 2

Multiply $y^{- 3}$ by $y^{4}$ by adding the exponents.

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Step 2.1

Move $y^{4}$ .

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

Step 2.2

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

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

Step 2.3

Subtract $3$ from $4$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Combine $5$ and $\frac{1}{x^{3}}$ .

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

Step 6

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

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Multiply $4$ by $5$ .

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