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

The quotient of the expression after simplification is .

The given parameters:

The quotient of the given expression is obtained by simplifying the expression as follows;

The quotient of the expression is written as follows;

Thus, the quotient of the expression after simplification is .

Learn more about law of indices here:  link

Step-by-step explanation:

We want to find the quotient of

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

This implies that:

We simplify exponents to get:

Or

Therefore the correct choice is

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).