Algebra Examples

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

Step 1

Multiply $x^{5}$ by $x^{- 3}$ by adding the exponents.

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Step 1.1

Move $x^{- 3}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 3$ and $5$ .

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

Step 2

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

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Step 2.1

Move $y^{3}$ .

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

Step 2.2

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

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

Step 2.3

Subtract $3$ from $3$ .

$4 x^{2} y^{0} \cdot - 3$

Step 3

Simplify $4 x^{2} y^{0} \cdot - 3$ .

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

Step 4

Multiply $- 3$ by $4$ .

$- 12 x^{2}$