Which expression is equivalent to $$ \frac{45 m^{-6} p^{2} v^{12}}{15 m^{-2} p^{8} v^{-4}} $$ for all values of $$ m, p $$, and $$ v $$ where the expression is defined? A. $$ \frac{3 v^{8}}{m^{8} p^{6}} $$ B. $$ \frac{3 v^{16}}{m^{4} p^{6}} $$ C. $$ \frac{30 m^{3}}{p^{4} v^{3}} $$ D. $$ \frac{30 v^{3}}{m^{3} p^{4}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{45 m^{-6} p^{2} v^{12}}{15 m^{-2} p^{8} v^{-4}}
$$

Follow these steps:

1. **Simplify the numerical coefficients:**
   $$
   \frac{45}{15} = 3
   $$

2. **Simplify each variable by subtracting the exponents in the denominator from those in the numerator:**
   - For $$ m $$:
     $$
     -6 - (-2) = -6 + 2 = -4 \quad \Rightarrow \quad m^{-4} = \frac{1}{m^4}
     $$
   - For $$ p $$:
     $$
     2 - 8 = -6 \quad \Rightarrow \quad p^{-6} = \frac{1}{p^6}
     $$
   - For $$ v $$:
     $$
     12 - (-4) = 12 + 4 = 16 \quad \Rightarrow \quad v^{16}
     $$

3. **Combine all parts together:**
   $$
   3 \times \frac{v^{16}}{m^4 p^6} = \frac{3 v^{16}}{m^4 p^6}
   $$

Therefore, the simplified expression is:

**Answer:** B. $$ \frac{3 v^{16}}{m^{4} p^{6}} $$
The simplified expression is $$ \frac{3 v^{16}}{m^{4} p^{6}} $$, which corresponds to option B.

Which expression is equivalent to for all values of , and where the expression is defined?
A.
B.
C.
D.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions

Which expression is equivalent to for all values of , and where the expression is defined? A. B. C. D.