Question

Select the correct answer Which is the correct simplified form of the expression (4m-2n^8)^1/2 ———— 9m^-6 n^-8

Answer 1

Answer:

$= \frac{2m^2n^8}{3}$

Step-by-step explanation:

Given expression is

$(\frac{4m^{-2}n^8}{9m^{-6}n^{-8}} )^{\frac{1}{2}$

The correct simplified form is shown below:-

From the above equation, we will simplify

we will shift $m^{-6}$ to the numerator and we will use the negative exponent rule, that is

$= (\frac{4m^{-2}n^8m^6}{9n^{-8}} )^{\frac{1}{2}$

now we will shift the $n^{-8}$ to the numerator and we will use the negative exponent rule, that is

$= (\frac{4m^{-2}n^8m^6n^8}{9} )^{\frac{1}{2}$

here we will solve the above equation which is shown below

$= (\frac{4m^4n^{16}}{9}) ^\frac{1}{2}$

So,

$= (\frac{(2)^2(m^2)^2(n^8)^2}{(3)^2} ^\frac{1}{2}$

Which gives result

$= \frac{2m^2n^8}{3}$