Calculus Examples

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

Step 1

Multiply $x^{5}$ by $x^{- 1}$ by adding the exponents.

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Step 1.1

Move $x^{- 1}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 1$ and $5$ .

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

Step 2

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

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Step 2.1

Move $y^{5}$ .

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

Step 2.2

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

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

Step 2.3

Add $5$ and $3$ .

$- 2 x^{4} y^{8} \cdot 3$

Step 3

Multiply $3$ by $- 2$ .

$- 6 x^{4} y^{8}$