Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 3

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

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Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y^{2}$ .

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Step 3.2.1

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

$4 (5^{2} {(x^{2})}^{2} (y^{1} y^{2})) {(2 x y^{3} z)}^{3} (x z)$

Step 3.2.2

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

$4 (5^{2} {(x^{2})}^{2} y^{1 + 2}) {(2 x y^{3} z)}^{3} (x z)$

Step 3.3

Add $1$ and $2$ .

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

Step 4

Raise $5$ to the power of $2$ .

$4 (25 {(x^{2})}^{2} y^{3}) {(2 x y^{3} z)}^{3} (x z)$

Step 5

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

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Step 5.1

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

$4 (25 x^{2 \cdot 2} y^{3}) {(2 x y^{3} z)}^{3} (x z)$

Step 5.2

Multiply $2$ by $2$ .

$4 (25 x^{4} y^{3}) {(2 x y^{3} z)}^{3} (x z)$

Step 6

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 6.1

Move $x$ .

$4 (25 (x \cdot x^{4}) y^{3}) {(2 x y^{3} z)}^{3} z$

Step 6.2

Multiply $x$ by $x^{4}$ .

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Step 6.2.1

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

$4 (25 (x^{1} x^{4}) y^{3}) {(2 x y^{3} z)}^{3} z$

Step 6.2.2

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

$4 (25 x^{1 + 4} y^{3}) {(2 x y^{3} z)}^{3} z$

Step 6.3

Add $1$ and $4$ .

$4 (25 x^{5} y^{3}) {(2 x y^{3} z)}^{3} z$

Step 7

Multiply $25$ by $4$ .

$100 (x^{5} y^{3}) {(2 x y^{3} z)}^{3} z$

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 $2 x y^{3} z$ .

$100 x^{5} y^{3} ({(2 x y^{3})}^{3} z^{3}) z$

Step 8.2

Apply the product rule to $2 x y^{3}$ .

$100 x^{5} y^{3} ({(2 x)}^{3} {(y^{3})}^{3} z^{3}) z$

Step 8.3

Apply the product rule to $2 x$ .

$100 x^{5} y^{3} (2^{3} x^{3} {(y^{3})}^{3} z^{3}) z$

Step 9

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

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Step 9.1

Move $x^{3}$ .

$100 (x^{3} x^{5}) y^{3} (2^{3} {(y^{3})}^{3} z^{3}) z$

Step 9.2

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

$100 x^{3 + 5} y^{3} (2^{3} {(y^{3})}^{3} z^{3}) z$

Step 9.3

Add $3$ and $5$ .

$100 x^{8} y^{3} (2^{3} {(y^{3})}^{3} z^{3}) z$

Step 10

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

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Step 10.1

Move $z$ .

$100 x^{8} y^{3} (2^{3} {(y^{3})}^{3} (z \cdot z^{3}))$

Step 10.2

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

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Step 10.2.1

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

$100 x^{8} y^{3} (2^{3} {(y^{3})}^{3} (z^{1} z^{3}))$

Step 10.2.2

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

$100 x^{8} y^{3} (2^{3} {(y^{3})}^{3} z^{1 + 3})$

Step 10.3

Add $1$ and $3$ .

$100 x^{8} y^{3} (2^{3} {(y^{3})}^{3} z^{4})$

Step 11

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

$100 x^{8} y^{3} (8 {(y^{3})}^{3} z^{4})$

Step 12

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

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Step 12.1

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

$100 x^{8} y^{3} (8 y^{3 \cdot 3} z^{4})$

Step 12.2

Multiply $3$ by $3$ .

$100 x^{8} y^{3} (8 y^{9} z^{4})$

Step 13

Multiply $y^{3}$ by $y^{9}$ by adding the exponents.

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Step 13.1

Move $y^{9}$ .

$100 x^{8} (y^{9} y^{3}) (8 z^{4})$

Step 13.2

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

$100 x^{8} y^{9 + 3} (8 z^{4})$

Step 13.3

Add $9$ and $3$ .

$100 x^{8} y^{12} (8 z^{4})$

Step 14

Multiply $8$ by $100$ .

$800 x^{8} y^{12} z^{4}$