Question

What is the simplified form of -24m^5n^4/8m^-7n^-2? Assume .m=0,n=0
A. 3/m^35 n^8
B.-3n^2/m^2
C.-3m^12 n^6
D. 3m^35 n^8

Answer 1

Answer:

Answer is  option 'D':  $-3m^{12} n^{6}$

Step-by-step explanation:

Step 1: Separate the different terms accordingly:

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

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

and then, simplify each of them and you should get the following procedures:

Step 1:

$\frac{-3}{1} \frac{m^{5-(-7)} }{1} \frac{n^{4-(-2)} }{1}$

basically shift the 'm' below to the above 'm' and their exponents subtract each other due to the rule of $\frac{a^{n} }{a^{m} } = \frac{a^{n-m} }{1} }$

Step 2:

$-3m^{5-(-7)} n^{4-(-2)}$

basically cancel out all the 1's below each of them

Step 3:

$-3m^{5+7} n^{4+2}$

the signs of exponents get reversed as there is a minus outside of the brackets.

Step 4 (answer):

$-3m^{12} n^{6}$

And that brings us to our answer of Option 'D'.

Thanks and hope you benefitted.