Basic Math Examples

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

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

Step 1

Combine.

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

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

Step 2

Multiply

z^{- 4}

$z^{- 4}$ by

z^{5}

$z^{5}$ by adding the exponents.

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Step 2.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 2.2

Add

- 4

$- 4$ and

5

$5$ .

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

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

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

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

Step 3

Simplify

z^{1}

$z^{1}$ .

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

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

Step 4

Multiply

z^{6}

$z^{6}$ by

z^{- 6}

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

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Step 4.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 4.2

Subtract

6

$6$ from

6

$6$ .

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

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

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

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

Step 5

Simplify

z^{0}

$z^{0}$ .

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

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

Step 6

Divide

z

$z$ by

1

$1$ .

z^{- 11}

$z^{- 11}$

Step 7

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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