Finite Math Examples

$\frac{3^{- 1} c^{- 2}}{{(3 c)}^{2}}$

Step 1

Raise to zero.

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Step 1.1

Move $3^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{c^{- 2}}{{(3 c)}^{2} \cdot 3}$

Step 1.2

Move $c^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(3 c)}^{2} \cdot 3 c^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $3 c$ .

$\frac{1}{3^{2} c^{2} \cdot 3 c^{2}}$

Step 2.2

Combine exponents.

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Step 2.2.1

Raise $3$ to the power of $1$ .

$\frac{1}{3^{1} \cdot 3^{2} c^{2} c^{2}}$

Step 2.2.2

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

$\frac{1}{3^{1 + 2} c^{2} c^{2}}$

Step 2.2.3

Add $1$ and $2$ .

$\frac{1}{3^{3} c^{2} c^{2}}$

Step 2.2.4

Multiply $c^{2}$ by $c^{2}$ by adding the exponents.

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Step 2.2.4.1

Move $c^{2}$ .

$\frac{1}{3^{3} (c^{2} c^{2})}$

Step 2.2.4.2

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

$\frac{1}{3^{3} c^{2 + 2}}$

Step 2.2.4.3

Add $2$ and $2$ .

$\frac{1}{3^{3} c^{4}}$

Step 2.3

Raise $3$ to the power of $3$ .

$\frac{1}{27 c^{4}}$