Pre-Algebra Examples

$\frac{{(2 m)}^{- 4}}{{(7 m)}^{- 5}}$

Step 1

Simplify the expression.

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Step 1.1

Move ${(2 m)}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(7 m)}^{- 5} {(2 m)}^{4}}$

Step 1.2

Move ${(7 m)}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(7 m)}^{5}}{{(2 m)}^{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $7 m$ .

$\frac{7^{5} m^{5}}{{(2 m)}^{4}}$

Step 2.2

Raise $7$ to the power of $5$ .

$\frac{16807 m^{5}}{{(2 m)}^{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $2 m$ .

$\frac{16807 m^{5}}{2^{4} m^{4}}$

Step 3.2

Raise $2$ to the power of $4$ .

$\frac{16807 m^{5}}{16 m^{4}}$

Step 4

Cancel the common factor of $m^{5}$ and $m^{4}$ .

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Step 4.1

Factor $m^{4}$ out of $16807 m^{5}$ .

$\frac{m^{4} (16807 m)}{16 m^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m^{4}$ out of $16 m^{4}$ .

$\frac{m^{4} (16807 m)}{m^{4} \cdot 16}$

Step 4.2.2

Cancel the common factor.

$\frac{m^{4} (16807 m)}{m^{4} \cdot 16}$

Step 4.2.3

Rewrite the expression.

$\frac{16807 m}{16}$