Algebra Examples

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

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 $3 x^{3} y^{5} z^{2}$ .

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

Step 1.2

Apply the product rule to $3 x^{3} y^{5}$ .

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

Step 1.3

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

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

Step 2

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

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Step 2.1

Move $3^{3}$ .

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

Step 2.2

Multiply $3^{3}$ by $3$ .

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Step 2.2.1

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

$3^{3} \cdot 3^{1} z ({(x^{3})}^{3} {(y^{5})}^{3} {(z^{2})}^{3}) {(x^{6} y z)}^{2}$

Step 2.2.2

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

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

Step 2.3

Add $3$ and $1$ .

$3^{4} z ({(x^{3})}^{3} {(y^{5})}^{3} {(z^{2})}^{3}) {(x^{6} y z)}^{2}$

Step 3

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

$81 z ({(x^{3})}^{3} {(y^{5})}^{3} {(z^{2})}^{3}) {(x^{6} y z)}^{2}$

Step 4

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

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Step 4.1

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

$81 z (x^{3 \cdot 3} {(y^{5})}^{3} {(z^{2})}^{3}) {(x^{6} y z)}^{2}$

Step 4.2

Multiply $3$ by $3$ .

$81 z (x^{9} {(y^{5})}^{3} {(z^{2})}^{3}) {(x^{6} y z)}^{2}$

Step 5

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

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Step 5.1

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

$81 z (x^{9} y^{5 \cdot 3} {(z^{2})}^{3}) {(x^{6} y z)}^{2}$

Step 5.2

Multiply $5$ by $3$ .

$81 z (x^{9} y^{15} {(z^{2})}^{3}) {(x^{6} y z)}^{2}$

Step 6

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

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Step 6.1

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

$81 z (x^{9} y^{15} z^{2 \cdot 3}) {(x^{6} y z)}^{2}$

Step 6.2

Multiply $2$ by $3$ .

$81 z (x^{9} y^{15} z^{6}) {(x^{6} y z)}^{2}$

Step 7

Multiply $z$ by $z^{6}$ by adding the exponents.

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Step 7.1

Move $z^{6}$ .

$81 (z^{6} z) (x^{9} y^{15}) {(x^{6} y z)}^{2}$

Step 7.2

Multiply $z^{6}$ by $z$ .

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Step 7.2.1

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

$81 (z^{6} z^{1}) (x^{9} y^{15}) {(x^{6} y z)}^{2}$

Step 7.2.2

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

$81 z^{6 + 1} (x^{9} y^{15}) {(x^{6} y z)}^{2}$

Step 7.3

Add $6$ and $1$ .

$81 z^{7} (x^{9} y^{15}) {(x^{6} y z)}^{2}$

Step 8

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

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Step 8.1

Apply the product rule to $x^{6} y z$ .

$81 z^{7} x^{9} y^{15} ({(x^{6} y)}^{2} z^{2})$

Step 8.2

Apply the product rule to $x^{6} y$ .

$81 z^{7} x^{9} y^{15} ({(x^{6})}^{2} y^{2} z^{2})$

Step 9

Multiply $z^{7}$ by $z^{2}$ by adding the exponents.

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Step 9.1

Move $z^{2}$ .

$81 (z^{2} z^{7}) x^{9} y^{15} ({(x^{6})}^{2} y^{2})$

Step 9.2

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

$81 z^{2 + 7} x^{9} y^{15} ({(x^{6})}^{2} y^{2})$

Step 9.3

Add $2$ and $7$ .

$81 z^{9} x^{9} y^{15} ({(x^{6})}^{2} y^{2})$

Step 10

Multiply $y^{15}$ by $y^{2}$ by adding the exponents.

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Step 10.1

Move $y^{2}$ .

$81 z^{9} x^{9} (y^{2} y^{15}) {(x^{6})}^{2}$

Step 10.2

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

$81 z^{9} x^{9} y^{2 + 15} {(x^{6})}^{2}$

Step 10.3

Add $2$ and $15$ .

$81 z^{9} x^{9} y^{17} {(x^{6})}^{2}$

Step 11

Multiply the exponents in ${(x^{6})}^{2}$ .

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Step 11.1

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

$81 z^{9} x^{9} y^{17} x^{6 \cdot 2}$

Step 11.2

Multiply $6$ by $2$ .

$81 z^{9} x^{9} y^{17} x^{12}$

Step 12

Multiply $x^{9}$ by $x^{12}$ by adding the exponents.

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Step 12.1

Move $x^{12}$ .

$81 z^{9} (x^{12} x^{9}) y^{17}$

Step 12.2

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

$81 z^{9} x^{12 + 9} y^{17}$

Step 12.3

Add $12$ and $9$ .

$81 z^{9} x^{21} y^{17}$