Basic Math Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

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 $- 2 a y^{2} z^{2}$ .

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

Step 2.2

Apply the product rule to $- 2 a y^{2}$ .

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

Step 2.3

Apply the product rule to $- 2 a$ .

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

Step 3

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

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Step 3.1

Move $a$ .

$2 ({(- 2)}^{3} (a \cdot a^{3}) {(y^{2})}^{3} {(z^{2})}^{3}) y^{3}$

Step 3.2

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

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Step 3.2.1

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

$2 ({(- 2)}^{3} (a^{1} a^{3}) {(y^{2})}^{3} {(z^{2})}^{3}) y^{3}$

Step 3.2.2

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

$2 ({(- 2)}^{3} a^{1 + 3} {(y^{2})}^{3} {(z^{2})}^{3}) y^{3}$

Step 3.3

Add $1$ and $3$ .

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

Step 4

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

$2 (- 8 a^{4} {(y^{2})}^{3} {(z^{2})}^{3}) y^{3}$

Step 5

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

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Step 5.1

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

$2 (- 8 a^{4} y^{2 \cdot 3} {(z^{2})}^{3}) y^{3}$

Step 5.2

Multiply $2$ by $3$ .

$2 (- 8 a^{4} y^{6} {(z^{2})}^{3}) y^{3}$

Step 6

Multiply $y^{6}$ by $y^{3}$ by adding the exponents.

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Step 6.1

Move $y^{3}$ .

$2 (- 8 a^{4} (y^{3} y^{6}) {(z^{2})}^{3})$

Step 6.2

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

$2 (- 8 a^{4} y^{3 + 6} {(z^{2})}^{3})$

Step 6.3

Add $3$ and $6$ .

$2 (- 8 a^{4} y^{9} {(z^{2})}^{3})$

Step 7

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

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Step 7.1

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

$2 (- 8 a^{4} y^{9} z^{2 \cdot 3})$

Step 7.2

Multiply $2$ by $3$ .

$2 (- 8 a^{4} y^{9} z^{6})$

Step 8

Multiply $- 8$ by $2$ .

$- 16 a^{4} y^{9} z^{6}$