Basic Math Examples

${(\frac{z^{- 4}}{z^{6}} \cdot \frac{z^{5}}{z^{- 6}})}^{- 11}$

Step 1

Combine.

${(\frac{z^{- 4} z^{5}}{z^{6} z^{- 6}})}^{- 11}$

Step 2

Multiply $z^{- 4}$ by $z^{5}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{z^{- 4 + 5}}{z^{6} z^{- 6}})}^{- 11}$

Step 2.2

Add $- 4$ and $5$ .

${(\frac{z^{1}}{z^{6} z^{- 6}})}^{- 11}$

Step 3

Simplify $z^{1}$ .

${(\frac{z}{z^{6} z^{- 6}})}^{- 11}$

Step 4

Multiply $z^{6}$ by $z^{- 6}$ by adding the exponents.

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Step 4.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{z}{z^{6 - 6}})}^{- 11}$

Step 4.2

Subtract $6$ from $6$ .

${(\frac{z}{z^{0}})}^{- 11}$

Step 5

Simplify $z^{0}$ .

${(\frac{z}{1})}^{- 11}$

Step 6

Divide $z$ by $1$ .

$z^{- 11}$

Step 7

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

$\frac{1}{z^{11}}$