Finite Math Examples

$\frac{{(3 m)}^{- 3}}{{(5 m)}^{- 5}}$

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

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

$\frac{{(5 m)}^{5}}{{(3 m)}^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $5 m$ .

$\frac{5^{5} m^{5}}{{(3 m)}^{3}}$

Step 2.2

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

$\frac{3125 m^{5}}{{(3 m)}^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $3 m$ .

$\frac{3125 m^{5}}{3^{3} m^{3}}$

Step 3.2

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

$\frac{3125 m^{5}}{27 m^{3}}$

Step 4

Cancel the common factor of $m^{5}$ and $m^{3}$ .

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Step 4.1

Factor $m^{3}$ out of $3125 m^{5}$ .

$\frac{m^{3} (3125 m^{2})}{27 m^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m^{3}$ out of $27 m^{3}$ .

$\frac{m^{3} (3125 m^{2})}{m^{3} \cdot 27}$

Step 4.2.2

Cancel the common factor.

$\frac{m^{3} (3125 m^{2})}{m^{3} \cdot 27}$

Step 4.2.3

Rewrite the expression.

$\frac{3125 m^{2}}{27}$