Algebra Examples

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

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 $- 3 x z^{5}$ .

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

Step 1.2

Apply the product rule to $- 3 x$ .

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $3$ .

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

Step 3

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

$- 2 x^{5} y (9 {(z^{5})}^{2}) {(x y^{3} z)}^{3}$

Step 4

Multiply the exponents in ${(z^{5})}^{2}$ .

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Step 4.1

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

$- 2 x^{5} y (9 z^{5 \cdot 2}) {(x y^{3} z)}^{3}$

Step 4.2

Multiply $5$ by $2$ .

$- 2 x^{5} y (9 z^{10}) {(x y^{3} z)}^{3}$

Step 5

Multiply $9$ by $- 2$ .

$- 18 x^{5} y z^{10} {(x y^{3} z)}^{3}$

Step 6

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

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Step 6.1

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

$- 18 x^{5} y z^{10} ({(x y^{3})}^{3} z^{3})$

Step 6.2

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

$- 18 x^{5} y z^{10} (x^{3} {(y^{3})}^{3} z^{3})$

Step 7

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

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Step 7.1

Move $x^{3}$ .

$- 18 (x^{3} x^{5}) y z^{10} ({(y^{3})}^{3} z^{3})$

Step 7.2

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

$- 18 x^{3 + 5} y z^{10} ({(y^{3})}^{3} z^{3})$

Step 7.3

Add $3$ and $5$ .

$- 18 x^{8} y z^{10} ({(y^{3})}^{3} z^{3})$

Step 8

Multiply $z^{10}$ by $z^{3}$ by adding the exponents.

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Step 8.1

Move $z^{3}$ .

$- 18 x^{8} y (z^{3} z^{10}) {(y^{3})}^{3}$

Step 8.2

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

$- 18 x^{8} y z^{3 + 10} {(y^{3})}^{3}$

Step 8.3

Add $3$ and $10$ .

$- 18 x^{8} y z^{13} {(y^{3})}^{3}$

Step 9

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

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Step 9.1

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

$- 18 x^{8} y z^{13} y^{3 \cdot 3}$

Step 9.2

Multiply $3$ by $3$ .

$- 18 x^{8} y z^{13} y^{9}$

Step 10

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

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Step 10.1

Move $y^{9}$ .

$- 18 x^{8} (y^{9} y) z^{13}$

Step 10.2

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

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Step 10.2.1

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

$- 18 x^{8} (y^{9} y^{1}) z^{13}$

Step 10.2.2

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

$- 18 x^{8} y^{9 + 1} z^{13}$

Step 10.3

Add $9$ and $1$ .

$- 18 x^{8} y^{10} z^{13}$