Question

What is the simplified form of StartFractio negative 24 m Superscript 5 Baseline n Superscript 4 Baseline Over 8 m Superscript negative 7 Baseline n Superscript negative 2 Baseline EndFraction? Assume m not-equals 0, n not-equals 0.

Answer 1

the answer is the option C.

hope this helps

Answer 2

Answer:

$\frac{-24m^5n^4}{8m^{-7}n^{-2}}=-3m^{12}n^{6}$

Step-by-step explanation:

Given:

The expression to simplify is given as:

$\frac{-24m^5n^4}{8m^{-7}n^{-2}}$

We have to simplify this using the properties of exponents.

The property that we use here is:

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

So, let us simplify the powers of $m\ and\ n$ separately and -24 and 8. This gives,

$\frac{m^5}{m^{-7}}=m^{5-(-7)}=m^{5+7}=m^{12}\\\frac{n^4}{n^{-2}}=n^{4-(-2)}=n^{4+2}=n^6\\\frac{-24}{8}=-3$

Therefore, the simplified form is:

$\frac{-24m^5n^4}{8m^{-7}n^{-2}}=-3m^{12}n^{6}$