Pre-Algebra Examples

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

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 $- 8 x y z^{4}$ .

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

Step 1.2

Apply the product rule to $- 8 x y$ .

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

Step 1.3

Apply the product rule to $- 8 x$ .

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

Step 2

Raise $- 8$ to the power of $2$ .

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

Step 3

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

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Step 3.1

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

$64 x^{2} y^{2} z^{4 \cdot 2}$

Step 3.2

Multiply $4$ by $2$ .

$64 x^{2} y^{2} z^{8}$