Precalculus Examples

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

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

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

Step 1.2

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

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

Step 1.3

Apply the product rule to $- x$ .

$- 3 x^{2} y^{3} z ({(- 1)}^{3} x^{3} {(y^{2})}^{3} {(z^{3})}^{3})$

Step 2

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

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Step 2.1

Move $x^{3}$ .

$- 3 (x^{3} x^{2}) y^{3} z ({(- 1)}^{3} {(y^{2})}^{3} {(z^{3})}^{3})$

Step 2.2

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

$- 3 x^{3 + 2} y^{3} z ({(- 1)}^{3} {(y^{2})}^{3} {(z^{3})}^{3})$

Step 2.3

Add $3$ and $2$ .

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

Step 3

Raise $- 1$ to the power of $3$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $2$ by $3$ .

$- 3 x^{5} y^{3} z (- 1 y^{6} {(z^{3})}^{3})$

Step 5

Multiply $y^{3}$ by $y^{6}$ by adding the exponents.

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Step 5.1

Move $y^{6}$ .

$- 3 x^{5} (y^{6} y^{3}) z (- 1 {(z^{3})}^{3})$

Step 5.2

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

$- 3 x^{5} y^{6 + 3} z (- 1 {(z^{3})}^{3})$

Step 5.3

Add $6$ and $3$ .

$- 3 x^{5} y^{9} z (- 1 {(z^{3})}^{3})$

Step 6

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

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Step 6.1

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

$- 3 x^{5} y^{9} z (- 1 z^{3 \cdot 3})$

Step 6.2

Multiply $3$ by $3$ .

$- 3 x^{5} y^{9} z (- 1 z^{9})$

Step 7

Multiply $z$ by $z^{9}$ by adding the exponents.

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Step 7.1

Move $z^{9}$ .

$- 3 x^{5} y^{9} (z^{9} z) \cdot - 1$

Step 7.2

Multiply $z^{9}$ by $z$ .

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Step 7.2.1

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

$- 3 x^{5} y^{9} (z^{9} z^{1}) \cdot - 1$

Step 7.2.2

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

$- 3 x^{5} y^{9} z^{9 + 1} \cdot - 1$

Step 7.3

Add $9$ and $1$ .

$- 3 x^{5} y^{9} z^{10} \cdot - 1$

Step 8

Multiply $- 1$ by $- 3$ .

$3 x^{5} y^{9} z^{10}$