Basic Math Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

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 $- 2 u^{3} y$ .

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

Step 2.2

Apply the product rule to $- 2 u^{3}$ .

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

Step 3

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

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Step 3.1

Move $y^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add $2$ and $2$ .

$2 ({(- 2)}^{2} {(u^{3})}^{2} y^{4}) u z^{3}$

Step 4

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

$2 (4 {(u^{3})}^{2} y^{4}) u z^{3}$

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $3$ by $2$ .

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

Step 6

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

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Step 6.1

Move $u$ .

$2 (4 (u \cdot u^{6}) y^{4}) z^{3}$

Step 6.2

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

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Step 6.2.1

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

$2 (4 (u^{1} u^{6}) y^{4}) z^{3}$

Step 6.2.2

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

$2 (4 u^{1 + 6} y^{4}) z^{3}$

Step 6.3

Add $1$ and $6$ .

$2 (4 u^{7} y^{4}) z^{3}$

Step 7

Multiply $4$ by $2$ .

$8 u^{7} y^{4} z^{3}$