Trigonometry Examples

$(5 a b) {(- 2 a^{2} b)}^{3}$

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 $- 2 a^{2} b$ .

$5 a b ({(- 2 a^{2})}^{3} b^{3})$

Step 1.2

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

$5 a b ({(- 2)}^{3} {(a^{2})}^{3} b^{3})$

Step 2

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

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Step 2.1

Move $b^{3}$ .

$5 a (b^{3} b) ({(- 2)}^{3} {(a^{2})}^{3})$

Step 2.2

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

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Step 2.2.1

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

$5 a (b^{3} b^{1}) ({(- 2)}^{3} {(a^{2})}^{3})$

Step 2.2.2

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

$5 a b^{3 + 1} ({(- 2)}^{3} {(a^{2})}^{3})$

Step 2.3

Add $3$ and $1$ .

$5 a b^{4} ({(- 2)}^{3} {(a^{2})}^{3})$

Step 3

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

$5 a b^{4} (- 8 {(a^{2})}^{3})$

Step 4

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

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Step 4.1

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

$5 a b^{4} (- 8 a^{2 \cdot 3})$

Step 4.2

Multiply $2$ by $3$ .

$5 a b^{4} (- 8 a^{6})$

Step 5

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

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Step 5.1

Move $a^{6}$ .

$5 (a^{6} a) b^{4} \cdot - 8$

Step 5.2

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

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Step 5.2.1

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

$5 (a^{6} a^{1}) b^{4} \cdot - 8$

Step 5.2.2

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

$5 a^{6 + 1} b^{4} \cdot - 8$

Step 5.3

Add $6$ and $1$ .

$5 a^{7} b^{4} \cdot - 8$

Step 6

Multiply $- 8$ by $5$ .

$- 40 a^{7} b^{4}$