Precalculus Examples

$\log_{3} ({(2 m)}^{- \frac{4}{3} \cdot {(4 m)}^{2}})$

Step 1

Apply the product rule to $4 m$ .

$\log_{3} ({(2 m)}^{- \frac{4}{3} \cdot (4^{2} m^{2})})$

Step 2

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

$\log_{3} ({(2 m)}^{- \frac{4}{3} \cdot (16 m^{2})})$

Step 3

Multiply $- \frac{4}{3} (16 m^{2})$ .

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Step 3.1

Multiply $16$ by $- 1$ .

$\log_{3} ({(2 m)}^{- 16 (\frac{4}{3}) m^{2}})$

Step 3.2

Combine $- 16$ and $\frac{4}{3}$ .

$\log_{3} ({(2 m)}^{\frac{- 16 \cdot 4}{3} m^{2}})$

Step 3.3

Multiply $- 16$ by $4$ .

$\log_{3} ({(2 m)}^{\frac{- 64}{3} m^{2}})$

Step 3.4

Combine $\frac{- 64}{3}$ and $m^{2}$ .

$\log_{3} ({(2 m)}^{\frac{- 64 m^{2}}{3}})$

Step 4

Move the negative in front of the fraction.

$\log_{3} ({(2 m)}^{- \frac{64 m^{2}}{3}})$

Step 5

Apply the product rule to $2 m$ .

$\log_{3} (2^{- \frac{64 m^{2}}{3}} m^{- \frac{64 m^{2}}{3}})$