Question

can anyone explain how to do radicals and fractions exponents.?

Answer 1

What do you want to know?

Answer 2

write an example of please

Answer 3

ok

Answer 4

Since exponents are shorthand for multiplication, they can have a variety of meanings

Answer 5

3 a-1/2 b3/2

Answer 6

ok so you good with\[ (a^2)^3=6?\]

Answer 7

kinda yea

Answer 8

so with fractional ones, let's break it up like that to start. \[3 a^{-1/2} b^{3/2}\\3(a^{-1})^{1/2}~(b^3)^{1/2}\]

Answer 9

@GREENDINO what are there please use parentheses

Answer 10

So if we multiplied we'd get what we started with right?

Answer 11

So you understand b^3 and a^-1 yea?

Answer 12

so i multiple the -1/2 ?

Answer 13

I am just taking it back a step. If we simplified,we would get what we started with. I want to make sure you understand we can do that.

Answer 14

ok yea i understand that

Answer 15

so, now, do you see how the top number of 3/2 is the number of times b is being multiplied to itself?

Answer 16

yes

Answer 17

So now the bottom number, is the root that requires 2 numbers to be pulled out (square root). You can also require 3 or 4 or what not, the roots will always be the bottom number of the fraction.

Answer 18

you might call these radicals. (square root)

Answer 19

yea

Answer 20

So now, what you have typed above can be written as \[3 a^{-1/2} b^{3/2}\\3(a^{-1})^{1/2}~(b^3)^{1/2}\\3\sqrt{a^{-1}}~~\sqrt{b^3}\]

Answer 21

Does that make sense?

Answer 22

so we just divided 1/2 so thats what made it 1?

Answer 23

We did n't divide anything

Answer 24

A square root is represented as 1/2 as an exponent.

Answer 25

rational exponents were invented so we didn't have to write out radicals all of the time. Also so we could use rules of exponents to simplify. Same with negative exponents being reciprocals. That was just a notional choice

Answer 26

notation*

Answer 27

ok i think i understand now, so what if its writen out like (2m)1/3 ?

Answer 28

So, what root requires 3 of the same thing in order to be removed?

Answer 29

square, cube, 4th, 5th, etc?

Answer 30

so it be 2 *2*2?

Answer 31

no, there is a 1 on top, so it is \[^3\sqrt{2m}\]

Answer 32

It is the cube root of two m.

Answer 33

so its just \[\sqrt{2m}\]

Answer 34

no, it's the cube root

Answer 35

the 3 on the bottom tells you it is a cube root. A cube root requires 3 of the same in order to be pulled out

Answer 36

\[^3\sqrt{2m}\]
Is how you would write this with a radical

Answer 37

2/3m

Answer 38

huh?

Answer 39

the 2 would b on top of the 3 with the m on the side of the problem ?

Answer 40

no. What I typed above is the representation.

Answer 41

there are two ways to write it. \[^3\sqrt{2m}=(2m)^{1/3}\]
Those are it.

Answer 42

so \[3\sqrt{2m}\] would be the answer ?

Answer 43

The 3 must be a little 3 that sits inside the radical's handle. This shows it is a cube root

Answer 44

And it's not an answer, just an equivalent way to write it.

Answer 45

oh ok

Answer 46

so some of the equations dont have answers like their answers are equations ?

Answer 47

does that make any sense ?

Answer 48

sort of, not really?

Answer 49

ok like how 5*5 =25


but (2m)1/3 is just \[3\sqrt{2m}\]

Answer 50

well it can't be simplified any further