Basic Math Examples

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

Step 1

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

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

Step 2

Combine $- 4$ and $\frac{1}{z^{2}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $- \frac{4}{z^{2}}$ .

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

Step 4.2

Apply the product rule to $\frac{4}{z^{2}}$ .

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

Step 5

Raise $- 1$ to the power of $6$ .

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

Step 6

Multiply $\frac{4^{6}}{{(z^{2})}^{6}}$ by $1$ .

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

Step 7

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

$\frac{4096}{{(z^{2})}^{6}}$

Step 8

Multiply the exponents in ${(z^{2})}^{6}$ .

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Step 8.1

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

$\frac{4096}{z^{2 \cdot 6}}$

Step 8.2

Multiply $2$ by $6$ .

$\frac{4096}{z^{12}}$