Question

How can I perform operations on exponents and powers? See below to see the solution.

Answer 1

Exponents in fractions:

MEDALS WOULD BE APPRECIATED. I will explain the basic properties of exponents and powers by using variables a,b, m and n.

Basic structure of exponents:
In the expression \[2^{3}\], 2 is the base and 3 is the exponent.This means that 2 is multiplied by itself 3 times. So, \[2^{3} = 2*2*2 = 8\].

Multiplying with the same base:
\[\LARGE a^{n} * a^{m} = a^{n+m}\]

Multiplying with the same exponent but different base:
\[\LARGE a^{n} * b{n} = {(a + b)^{n}} \]

Dividing with the same base:
\[\LARGE {{a^{m}} \over {a^{n}} = {a}^{m-n}}\]

Multiplying an exponent by an exponent:
\[\LARGE {(a^{m})^{n}} = {a ^ {mn}} \]

Note that we cannot simply get the value of:
\[ \LARGE {a^{m}} - {a^{n}} \] or \[ {a^{m}} + {a^{n}} \]

Exponents in negative:
\[\LARGE {a ^{-m}} = {1 \over a^{m}}\]

Exponents in fractions:
\[\LARGE {a ^ {1 \over m}} = \sqrt[m]{a}\]

Answer 2

\[a^{n}*bn=(a+b)^{n}\] ? please explain

Answer 3

I meant a^n * b^n

Answer 4

Also, dividing by the same base has an error.

Answer 5

wouldn't it be a^n+nab+b^n

Answer 6

follow the laws of exponent

Answer 7

i think i disagree that \(\large a^n \times b^n = (a+b)^n\)

assuming n = 2...

\((a+b)^2 = a^2 + 2ab + b^2 \ne (a^2 \times b^2)\)

Answer 8

but anyways good job :)

Answer 9

Yes, I forgot to put that one in. I also tried that last year.

Answer 10

yes, PK is doing good stuff here

Answer 11

\[\LARGE {a^{m} \over a^{n}} = {a^{m - n}} \]

Answer 12

i also disagree that \(\Large (a+b)^n = a^n + nab + b^n\) lol...it only works in square..

for example \((a+b)^3 \ne a^3 + 3ab + b^3\) since \((a+b)^3 = (a^2 + 2ab + b^2)(a+b)\).

just clearing the misconceptions :D so there is no rule for \(\large a^n \times b^n\)

Answer 13

Another pattern that I noticed is that if a<m and a and m are more 2,

\[\LARGE a^{m} > m^{a}\]

Answer 14

good job

Answer 15

well there is..it's simply \(a^n b^n\)

Answer 16

I suck at tutorials lol

Answer 17

nahh it's fine :DDD you'll get there hehe

Answer 18

remember that these corrections are not critics..they are merely for references

Answer 19

I could have easily written this on paper, but in latex there are lotta errors :P... Thanks lg. I hope you like my badly written yet fair tutorials.

Answer 20

you might wanna add this:

\(\LARGE a^{\frac{n}{m}} = \sqrt[m]{a^n}\)

Answer 21

See the last one bro.. there it is.

Answer 22

nahh..you only put 1/m :P hehe

Answer 23

Oh yeah. :D

Answer 24

and yes i do like it :) i couldnt have listed all of those down myself..i have poor memory ahah..this can help a lot of people so keep bumping it

Answer 25

=)

Answer 26

\[a^n \times b^n \neq (a+b)^n\]
But
\[a^n \times b^n = (ab)^n\]
I think only :)

Answer 27

Haha the latex confused me so much that I got the math wrong. Thanks for correcting me :)

Answer 28

You're welcome