Algebra Examples

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

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $4 x y$ .

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

Step 1.2

Apply the product rule to $4 x$ .

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $2$ and $1$ .

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

Step 3

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

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Step 3.1

Move $y^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add $2$ and $3$ .

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

Step 4

Raise $4$ to the power of $2$ .

$- 3 x^{3} y^{5} \cdot 16$

Step 5

Multiply $16$ by $- 3$ .

$- 48 x^{3} y^{5}$