Question

Why is:
\[\Large {x ^ {-m}} = {1 \over x^{m}}\]
Note that x is not equal to 0.
See below for the explanation.

Answer 1

I'm gonna explain it to you in illustrations. MEDALS APPRECIATED.
\[\Large \text{Illustration 1: }{{x^{x + 1} \over x} = x ^{x}}\]
We have to agree, right? We know that when we divide two exponents with the same base, the powers subtract.
Let's take an example of this.
\[\Large {2^{3} \over 2} = 2^{2}} \]
\[\Large \text{Illustration 2: } {x^{1} = x} \]
We all know this one, right?
\[\Large \text{Illustration 3: }{x^{0} = 1} \]
Why is this so? See illustration 1 again and try to figure it out. (Hint, you can simply substitute x with 0.)

\[\Large \text{Illutration 4:}{x^{-m} = {1 \over x^{m}}}\]

Now, let us again see the illustration 1 and learn how it goes.
Let's take an example of \[10^{-1}\]

We know that \[x^{0} = 1\].

Inferring from example 1 and substituting x with -1, we can say:
\[\Large {1 \over 10^{1}} = 10^{-1}\]

\[\Large \text{ANOTHER WAY TO EXPLAIN}\]

Taking an example of 5, we say that as the exponent decreases, we divide by 5.

1)25(which is 5 squared) divided by 5 = 5(which is 5 to the first power)
2)5(5 to the first power) divided by 5 = 1(5 to the zeroth power)
3)1(5 to the zeroth power) divided by 5 = 1 over 5(1 over 5 to the first power)

Answer 2

\[\Large {2 ^ {3} \over 2} = 2^{2} \]

Answer 3

\[x ^{m} \times x ^{-m}=1 that means x ^{m+(-m)}= x ^{0}=1\]

Answer 4

A good example. But, that won't explain everything.

Answer 5

get some good sort of qns

Answer 6

This is a tutorial.

Answer 7

u got ur ans or not finally

Answer 8

THIS is a TUTORIAL, not a question.

Answer 9

can u elaborate tutorial meaning pls

Answer 10

Tutorial is an explanation of how to do something.

Answer 11

operate x^m on both the sides and apply algebra

Answer 12

I know, I'm explaining it WHY

Answer 13

you should mention in your tutorial that this does not work for \(x=0\)

Answer 14

I tried to explain it this way.