HELP

Thanks DS that is a great answer.  You should give yourself 5 points too  :D

 

DS is right, it really depends on what you are doing.

 

the opposite of squaring something is squarerooting it

so

 

\((\sqrt{x})^2=(x^{1/2})^2=x^{2/2}=x\\~\\ or\\~\\ (x^{-4.5})^{-1/4.5}=x \)

Here is a link:

https://answers.yahoo.com/question/index?qid=20070909181046AAmfZkI

 

And here is an explanation, from Yahoo Answers:

 

Explanation 1)

The inverse operation of exponents IS root. 
To reduce an exponent from 2 to 1, we must divide it by 2. 
Therefore, if 
m^2 = 144, then 
m^(2*1/2) = 144^(1/2) 
m^1 = 144^(1/2) 
m = square root of 144 

Similarly, if you have m^3 = something, then you take the cube root. For m^4 = something, then the fourth root, and so on. 

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One way to imagine another "inverse" operation is to use logarithms (a.k.a., logs). To use logs, you need a base and powers to which you raise that base. A commonly used base is 10 (simply because we, humans, like to use the decimal system). 

Normally, we are used to see 10 raised to whole number powers: 

10^1 = 10 (anything to power 1 is itself) 
10^2 = 100 (10^2 means 10*10) 
10^3 = 1000 (10^3 = 10*10*10) 
and so on 

what about 
10^2.5 
Well it is the same as 10^2 * 10^(1/2) = 100 * SQRT(10) 
(316.22777...) 
10^2.2 = 10^2 times 10^0.2 = 100 times fifth root of 10 = 158.489... 

It is possible to calculate values for all possible powers of 10 (and tables had been prepared as far back as the early 1600s. 

10^2.1583625 = 144 
We say: the log of 144 (in base 10) is 2.1583625 -- with more or less decimals, depending on the degree of accuracy we need. 

m^2 = 144 = 10^2.1583625 
then 
m^1 = 144^0.5 = 10^(2.1583625/2) = 10^1.0791813 

Looking up 10^1.0791813 in a logarithm table, one finds that it is 12. 
"The antilog of 1.0791813 is 12" 

Computers (and most calculators) perform root calculations by using "natural" logarithms where the base is 2.718281828459..., a number represented by the letter e. 

In advanced math, e has special properties. For example, the differential of e^x is e^x AND the integral of e^x is e^x (+ a constant). 

However, it is much easier to find a written table of "common" logs (base 10) than one in any other base.

 

Explanation 2) 

If the exponent is 2, the inverse is the exponent 1/2.

144^(1/2) = 12

 

I HOPE THIS HELPED!