Algebra Examples

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

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 $3 x y$ .

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

Step 1.2

Apply the product rule to $3 x$ .

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

Step 2

Raise $3$ to the power of $2$ .

$9 x^{2} y^{2} \cdot {(- 4 x^{3} y^{2})}^{3}$

Step 3

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

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Step 3.1

Apply the product rule to $- 4 x^{3} y^{2}$ .

$9 x^{2} y^{2} \cdot ({(- 4 x^{3})}^{3} {(y^{2})}^{3})$

Step 3.2

Apply the product rule to $- 4 x^{3}$ .

$9 x^{2} y^{2} \cdot ({(- 4)}^{3} {(x^{3})}^{3} {(y^{2})}^{3})$

Step 4

Raise $- 4$ to the power of $3$ .

$9 x^{2} y^{2} \cdot (- 64 {(x^{3})}^{3} {(y^{2})}^{3})$

Step 5

Multiply the exponents in ${(x^{3})}^{3}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$9 x^{2} y^{2} \cdot (- 64 x^{3 \cdot 3} {(y^{2})}^{3})$

Step 5.2

Multiply $3$ by $3$ .

$9 x^{2} y^{2} \cdot (- 64 x^{9} {(y^{2})}^{3})$

Step 6

Multiply $x^{2}$ by $x^{9}$ by adding the exponents.

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Step 6.1

Move $x^{9}$ .

$9 (x^{9} x^{2}) y^{2} \cdot (- 64 {(y^{2})}^{3})$

Step 6.2

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

$9 x^{9 + 2} y^{2} \cdot (- 64 {(y^{2})}^{3})$

Step 6.3

Add $9$ and $2$ .

$9 x^{11} y^{2} \cdot (- 64 {(y^{2})}^{3})$

Step 7

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$9 x^{11} y^{2} \cdot (- 64 y^{2 \cdot 3})$

Step 7.2

Multiply $2$ by $3$ .

$9 x^{11} y^{2} \cdot (- 64 y^{6})$

Step 8

Multiply $y^{2}$ by $y^{6}$ by adding the exponents.

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Step 8.1

Move $y^{6}$ .

$9 x^{11} (y^{6} y^{2}) \cdot - 64$

Step 8.2

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

$9 x^{11} y^{6 + 2} \cdot - 64$

Step 8.3

Add $6$ and $2$ .

$9 x^{11} y^{8} \cdot - 64$

Step 9

Multiply $- 64$ by $9$ .

$- 576 x^{11} y^{8}$