Algebra Examples

$\frac{12 m^{2}}{{(4 m)}^{- 4}}$

Step 1

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

$12 m^{2} {(4 m)}^{4}$

Step 2

Apply the product rule to $4 m$ .

$12 m^{2} (4^{4} m^{4})$

Step 3

Rewrite using the commutative property of multiplication.

$12 \cdot 4^{4} m^{2} m^{4}$

Step 4

Multiply $m^{2}$ by $m^{4}$ by adding the exponents.

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Step 4.1

Move $m^{4}$ .

$12 \cdot 4^{4} (m^{4} m^{2})$

Step 4.2

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

$12 \cdot 4^{4} m^{4 + 2}$

Step 4.3

Add $4$ and $2$ .

$12 \cdot 4^{4} m^{6}$

Step 5

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

$12 \cdot 256 m^{6}$

Step 6

Multiply $12$ by $256$ .

$3072 m^{6}$