Precalculus Examples

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

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 $4 x^{2} y^{4}$ .

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

Step 1.2

Apply the product rule to $4 x^{2}$ .

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

Step 2

Raise $4$ to the power of $3$ .

$64 {(x^{2})}^{3} {(y^{4})}^{3}$

Step 3

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

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Step 3.1

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

$64 x^{2 \cdot 3} {(y^{4})}^{3}$

Step 3.2

Multiply $2$ by $3$ .

$64 x^{6} {(y^{4})}^{3}$

Step 4

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

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Step 4.1

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

$64 x^{6} y^{4 \cdot 3}$

Step 4.2

Multiply $4$ by $3$ .

$64 x^{6} y^{12}$