Algebra Examples

${(x^{5} y^{2})}^{3} {(- 3 x^{3} y^{5})}^{2} (2 x z^{6})$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(x^{5} y^{2})}^{3} {(- 3 x^{3} y^{5})}^{2} (x z^{6})$

Step 2

Apply the product rule to $x^{5} y^{2}$ .

$2 ({(x^{5})}^{3} {(y^{2})}^{3}) {(- 3 x^{3} y^{5})}^{2} (x z^{6})$

Step 3

Multiply the exponents in ${(x^{5})}^{3}$ .

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Step 3.1

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

$2 (x^{5 \cdot 3} {(y^{2})}^{3}) {(- 3 x^{3} y^{5})}^{2} (x z^{6})$

Step 3.2

Multiply $5$ by $3$ .

$2 (x^{15} {(y^{2})}^{3}) {(- 3 x^{3} y^{5})}^{2} (x z^{6})$

Step 4

Multiply $x^{15}$ by $x$ by adding the exponents.

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Step 4.1

Move $x$ .

$2 (x \cdot x^{15} {(y^{2})}^{3}) {(- 3 x^{3} y^{5})}^{2} z^{6}$

Step 4.2

Multiply $x$ by $x^{15}$ .

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Step 4.2.1

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

$2 (x^{1} x^{15} {(y^{2})}^{3}) {(- 3 x^{3} y^{5})}^{2} z^{6}$

Step 4.2.2

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

$2 (x^{1 + 15} {(y^{2})}^{3}) {(- 3 x^{3} y^{5})}^{2} z^{6}$

Step 4.3

Add $1$ and $15$ .

$2 (x^{16} {(y^{2})}^{3}) {(- 3 x^{3} y^{5})}^{2} z^{6}$

Step 5

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

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Step 5.1

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

$2 (x^{16} y^{2 \cdot 3}) {(- 3 x^{3} y^{5})}^{2} z^{6}$

Step 5.2

Multiply $2$ by $3$ .

$2 (x^{16} y^{6}) {(- 3 x^{3} y^{5})}^{2} z^{6}$

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

$2 x^{16} y^{6} ({(- 3 x^{3})}^{2} {(y^{5})}^{2}) z^{6}$

Step 6.2

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

$2 x^{16} y^{6} ({(- 3)}^{2} {(x^{3})}^{2} {(y^{5})}^{2}) z^{6}$

Step 7

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

$2 x^{16} y^{6} (9 {(x^{3})}^{2} {(y^{5})}^{2}) z^{6}$

Step 8

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

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Step 8.1

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

$2 x^{16} y^{6} (9 x^{3 \cdot 2} {(y^{5})}^{2}) z^{6}$

Step 8.2

Multiply $3$ by $2$ .

$2 x^{16} y^{6} (9 x^{6} {(y^{5})}^{2}) z^{6}$

Step 9

Multiply $x^{16}$ by $x^{6}$ by adding the exponents.

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Step 9.1

Move $x^{6}$ .

$2 (x^{6} x^{16}) y^{6} (9 {(y^{5})}^{2}) z^{6}$

Step 9.2

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

$2 x^{6 + 16} y^{6} (9 {(y^{5})}^{2}) z^{6}$

Step 9.3

Add $6$ and $16$ .

$2 x^{22} y^{6} (9 {(y^{5})}^{2}) z^{6}$

Step 10

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

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Step 10.1

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

$2 x^{22} y^{6} (9 y^{5 \cdot 2}) z^{6}$

Step 10.2

Multiply $5$ by $2$ .

$2 x^{22} y^{6} (9 y^{10}) z^{6}$

Step 11

Multiply $y^{6}$ by $y^{10}$ by adding the exponents.

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Step 11.1

Move $y^{10}$ .

$2 x^{22} (y^{10} y^{6}) \cdot 9 z^{6}$

Step 11.2

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

$2 x^{22} y^{10 + 6} \cdot 9 z^{6}$

Step 11.3

Add $10$ and $6$ .

$2 x^{22} y^{16} \cdot 9 z^{6}$

Step 12

Multiply $9$ by $2$ .

$18 x^{22} y^{16} z^{6}$