Finite Math Examples

${(\frac{x^{6} v}{z f^{6}})}^{- 6}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{z f^{6}}{x^{6} v})}^{6}$

Step 2

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

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Step 2.1

Apply the product rule to $\frac{z f^{6}}{x^{6} v}$ .

$\frac{{(z f^{6})}^{6}}{{(x^{6} v)}^{6}}$

Step 2.2

Apply the product rule to $z f^{6}$ .

$\frac{z^{6} {(f^{6})}^{6}}{{(x^{6} v)}^{6}}$

Step 2.3

Apply the product rule to $x^{6} v$ .

$\frac{z^{6} {(f^{6})}^{6}}{{(x^{6})}^{6} v^{6}}$

Step 3

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

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Step 3.1

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

$\frac{z^{6} f^{6 \cdot 6}}{{(x^{6})}^{6} v^{6}}$

Step 3.2

Multiply $6$ by $6$ .

$\frac{z^{6} f^{36}}{{(x^{6})}^{6} v^{6}}$

Step 4

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

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Step 4.1

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

$\frac{z^{6} f^{36}}{x^{6 \cdot 6} v^{6}}$

Step 4.2

Multiply $6$ by $6$ .

$\frac{z^{6} f^{36}}{x^{36} v^{6}}$