Algebra Examples

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

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 $3 x^{2} y z^{4}$ .

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

Step 1.2

Apply the product rule to $3 x^{2} y$ .

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

Step 1.3

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

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

Step 2

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

$9 {(x^{2})}^{2} y^{2} {(z^{4})}^{2}$

Step 3

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

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Step 3.1

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

$9 x^{2 \cdot 2} y^{2} {(z^{4})}^{2}$

Step 3.2

Multiply $2$ by $2$ .

$9 x^{4} y^{2} {(z^{4})}^{2}$

Step 4

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

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Step 4.1

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

$9 x^{4} y^{2} z^{4 \cdot 2}$

Step 4.2

Multiply $4$ by $2$ .

$9 x^{4} y^{2} z^{8}$