What is the inverse operation of exponents?

Question

Besides square roots how would you solve the problem
m squared = 144 i need to be able to cancel out the m squared part and do the same to 144 to get the obvious answer 12

Answer 1

if the exponent is 3, the inverse is the exponent 1/3

144^(1/2) = 12

Answer 2

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.

Answer 3

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RE:
What is the inverse operation of exponents?
Besides square roots how would you solve the problem
m squared = 144 i need to be able to cancel out the m squared part and do the same to 144 to get the obvious answer 12

Answer 4

Opposite Of Exponent

Answer 5

What Is An Inverse Operation

Answer 6

How about using a calculator

first take log 144 = 21.5
divide by 2 = 1.079
10^x = 12

Answer 7

You may use logarithms
M^2 = 144
ln(M^2) = ln(144)
2*ln(M) = ln(144)
ln(M) = ln(144)/2
exp(ln(M)) = exp(ln(144)/2)
M = exp(2.48490) = 12