Pre-Algebra Examples

$4 z^{- 7} \cdot (2^{- 2} {(z^{2})}^{2})$

Step 1

Rewrite using the commutative property of multiplication.

$4 \cdot 2^{- 2} z^{- 7} {(z^{2})}^{2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 \cdot \frac{1}{2^{2}} z^{- 7} {(z^{2})}^{2}$

Step 3

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

$4 \cdot \frac{1}{4} z^{- 7} {(z^{2})}^{2}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Cancel the common factor.

$4 \cdot \frac{1}{4} z^{- 7} {(z^{2})}^{2}$

Step 4.2

Rewrite the expression.

$1 z^{- 7} {(z^{2})}^{2}$

Step 5

Multiply $z^{- 7}$ by $1$ .

$z^{- 7} {(z^{2})}^{2}$

Step 6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{z^{7}} {(z^{2})}^{2}$

Step 7

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

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Step 7.1

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

$\frac{1}{z^{7}} z^{2 \cdot 2}$

Step 7.2

Multiply $2$ by $2$ .

$\frac{1}{z^{7}} z^{4}$

Step 8

Cancel the common factor of $z^{4}$ .

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Step 8.1

Factor $z^{4}$ out of $z^{7}$ .

$\frac{1}{z^{4} z^{3}} z^{4}$

Step 8.2

Cancel the common factor.

$\frac{1}{z^{4} z^{3}} z^{4}$

Step 8.3

Rewrite the expression.

$\frac{1}{z^{3}}$