Question

What is the quotient StartFraction 2 m Superscript 9 Baseline n Superscript 4 Baseline Over Negative 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline EndFractionin simplest form? Assume m not-equals 0, n not-equals 0.
Negative StartFraction m Superscript 12 Baseline n Superscript 6 Baseline Over 2 EndFraction
Negative StartFraction m Superscript 27 Baseline n Superscript 8 Baseline Over 2 EndFraction
6 m Superscript 12 Baseline n Superscript 6 Baseline
8 m Superscript 12 Baseline n Superscript 6 Baseline

Answer 1

Answer:

$-\frac{m^{12}n^{6}}{2}$

Step-by-step explanation:

We want to find the quotient of $\frac{2m^9n^4}{-4m^{-3}n^{-2}}$

We apply the quotient rule of indices to simplify the given exponential expression.

$\frac{a^m}{a^n}=a^{m-n}$

This implies that:

$\frac{2m^9n^4}{-4m^{-3}n^{-2}}=-\frac{1}{2}m^{9--3}n^{4--2}$

We simplify exponents to get:

$\frac{2m^9n^4}{-4m^{-3}n^{-2}}=-\frac{1}{2}m^{12}n^{6}$

Or

$\frac{2m^9n^4}{-4m^{-3}n^{-2}}=-\frac{m^{12}n^{6}}{2}$

Therefore the correct choice is $-\frac{m^{12}n^{6}}{2}$

Answer 2

Answer:

-\frac{m^{12}n^{6}}{2}

You got this!!