Basic Math Examples

$\frac{{(5 c)}^{- 2}}{{(3 c)}^{- 3}}$

Step 1

Simplify the expression.

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Step 1.1

Move ${(5 c)}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(3 c)}^{- 3} {(5 c)}^{2}}$

Step 1.2

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

$\frac{{(3 c)}^{3}}{{(5 c)}^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $3 c$ .

$\frac{3^{3} c^{3}}{{(5 c)}^{2}}$

Step 2.2

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

$\frac{27 c^{3}}{{(5 c)}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $5 c$ .

$\frac{27 c^{3}}{5^{2} c^{2}}$

Step 3.2

Raise $5$ to the power of $2$ .

$\frac{27 c^{3}}{25 c^{2}}$

Step 4

Cancel the common factor of $c^{3}$ and $c^{2}$ .

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Step 4.1

Factor $c^{2}$ out of $27 c^{3}$ .

$\frac{c^{2} (27 c)}{25 c^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $c^{2}$ out of $25 c^{2}$ .

$\frac{c^{2} (27 c)}{c^{2} \cdot 25}$

Step 4.2.2

Cancel the common factor.

$\frac{c^{2} (27 c)}{c^{2} \cdot 25}$

Step 4.2.3

Rewrite the expression.

$\frac{27 c}{25}$