How to solve?

Question

Find the square root of the positive variables.

1. The negative square root of a^2b^4c^12

Answer 1

The answer is -a^48bc.

If an exponent is raised to another exponent, you can multiply the exponents, for example

(2^2)^3 = 2^(2*3)

so in this problem,
((a^2b)^4c)^12 = a^(2b*4c*12) = a^96bc

A square root is the same as raising something to the power of (1/2), so -(a^96bc)^(1/2) = -a^(96bc*(1/2)) = -a^48bc

Answer 2

negative exponents means you put the expression over 1

2^(-2) = 1/4

x^(-1)=1/x

16^(-1/2) = 1/4 this is a negative square root
the negative square root of 16 is 1/4

so

(a^2b^4c^12)^(-1/2) =
(a^2)^(-1/2) x (b^4)^(-1/2) x (c^12)^(-1/2)
when you raise an expoent to a power, you multiply the exponents, so:
(a^-1)(b^-2)(c^-6)=
1/(ab^2c^6)

I hope this helps

Answer 3

taking the square root halves the power, so a^(2/2)=a so repeat for the other variables.
then you take the opposite of that cuz its the negative square root:
-ab^2c^6

Answer 4

aabbbbcccccc
= (abbccc)(abbccc) by the associative property
= (ab^2c^3)^2
so negative square root is -(ab^2c^3)