Finite Math Examples

${(3 x^{3} y^{2})}^{3} {(- 2 x y^{7})}^{2}$

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 $3 x^{3} y^{2}$ .

${(3 x^{3})}^{3} {(y^{2})}^{3} {(- 2 x y^{7})}^{2}$

Step 1.2

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

$3^{3} {(x^{3})}^{3} {(y^{2})}^{3} {(- 2 x y^{7})}^{2}$

Step 2

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

$27 {(x^{3})}^{3} {(y^{2})}^{3} {(- 2 x y^{7})}^{2}$

Step 3

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

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Step 3.1

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

$27 x^{3 \cdot 3} {(y^{2})}^{3} {(- 2 x y^{7})}^{2}$

Step 3.2

Multiply $3$ by $3$ .

$27 x^{9} {(y^{2})}^{3} {(- 2 x y^{7})}^{2}$

Step 4

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

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Step 4.1

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

$27 x^{9} y^{2 \cdot 3} {(- 2 x y^{7})}^{2}$

Step 4.2

Multiply $2$ by $3$ .

$27 x^{9} y^{6} {(- 2 x y^{7})}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $- 2 x y^{7}$ .

$27 x^{9} y^{6} ({(- 2 x)}^{2} {(y^{7})}^{2})$

Step 5.2

Apply the product rule to $- 2 x$ .

$27 x^{9} y^{6} ({(- 2)}^{2} x^{2} {(y^{7})}^{2})$

Step 6

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

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Step 6.1

Move $x^{2}$ .

$27 (x^{2} x^{9}) y^{6} ({(- 2)}^{2} {(y^{7})}^{2})$

Step 6.2

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

$27 x^{2 + 9} y^{6} ({(- 2)}^{2} {(y^{7})}^{2})$

Step 6.3

Add $2$ and $9$ .

$27 x^{11} y^{6} ({(- 2)}^{2} {(y^{7})}^{2})$

Step 7

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

$27 x^{11} y^{6} (4 {(y^{7})}^{2})$

Step 8

Multiply the exponents in ${(y^{7})}^{2}$ .

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Step 8.1

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

$27 x^{11} y^{6} (4 y^{7 \cdot 2})$

Step 8.2

Multiply $7$ by $2$ .

$27 x^{11} y^{6} (4 y^{14})$

Step 9

Multiply $y^{6}$ by $y^{14}$ by adding the exponents.

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Step 9.1

Move $y^{14}$ .

$27 x^{11} (y^{14} y^{6}) \cdot 4$

Step 9.2

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

$27 x^{11} y^{14 + 6} \cdot 4$

Step 9.3

Add $14$ and $6$ .

$27 x^{11} y^{20} \cdot 4$

Step 10

Multiply $4$ by $27$ .

$108 x^{11} y^{20}$