Trigonometry Examples

${(- 2 x^{2} y^{3})}^{4}$

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 $- 2 x^{2} y^{3}$ .

${(- 2 x^{2})}^{4} {(y^{3})}^{4}$

Step 1.2

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

${(- 2)}^{4} {(x^{2})}^{4} {(y^{3})}^{4}$

Step 2

Raise $- 2$ to the power of $4$ .

$16 {(x^{2})}^{4} {(y^{3})}^{4}$

Step 3

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 3.1

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

$16 x^{2 \cdot 4} {(y^{3})}^{4}$

Step 3.2

Multiply $2$ by $4$ .

$16 x^{8} {(y^{3})}^{4}$

Step 4

Multiply the exponents in ${(y^{3})}^{4}$ .

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Step 4.1

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

$16 x^{8} y^{3 \cdot 4}$

Step 4.2

Multiply $3$ by $4$ .

$16 x^{8} y^{12}$