Basic Math Examples

${(6 z^{- 1})}^{4} {(z^{5})}^{- 2}$

Step 1

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

${(6 \frac{1}{z})}^{4} {(z^{5})}^{- 2}$

Step 2

Combine $6$ and $\frac{1}{z}$ .

${(\frac{6}{z})}^{4} {(z^{5})}^{- 2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{6}{z}$ .

$\frac{6^{4}}{z^{4}} {(z^{5})}^{- 2}$

Step 3.2

Raise $6$ to the power of $4$ .

$\frac{1296}{z^{4}} {(z^{5})}^{- 2}$

Step 3.3

Multiply the exponents in ${(z^{5})}^{- 2}$ .

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Step 3.3.1

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

$\frac{1296}{z^{4}} z^{5 \cdot - 2}$

Step 3.3.2

Multiply $5$ by $- 2$ .

$\frac{1296}{z^{4}} z^{- 10}$

Step 4

Cancel the common factor of $z^{- 10}$ .

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Step 4.1

Factor $z^{- 10}$ out of $z^{4}$ .

$\frac{1296}{z^{- 10} z^{14}} z^{- 10}$

Step 4.2

Cancel the common factor.

$\frac{1296}{z^{- 10} z^{14}} z^{- 10}$

Step 4.3

Rewrite the expression.

$\frac{1296}{z^{14}}$