Question

(√(2m)^-3)/(m^-1)

Answer 1

do you want to clear for m?

Answer 2

I want to simplify.

Answer 3

http://www.quickmath.com/webMathematica3/quickmath/algebra/simplify/basic.jsp#c=simplify_stepssimplify&v1=(%E2%88%9A(2m)%5E-3)%2F(m%5E-1)+

Answer 4

ok so \[\frac{ \sqrt{2m}^{-3} }{ m ^{-1} }\]

Answer 5

The 2m is in parentheses.

Answer 6

@Ashy98 you know you have to use your brain?

Answer 7

yeah, thats why the root is working for the whole thing

Answer 8

\[√(2m)^-3\]

Answer 9

yeah @SalvadorV but that helps just a little!

Answer 10

you start by passing the m^-1 which is dividing, up as m^1 or just m

Answer 11

well, this is to learn, not just to have someone finish your homework @Ashy98

Answer 12

a1234, if the sqrt is being applied to 2m, it is the same as having it in a parentheses

Answer 13

Won't 2^3 be done then?

Answer 14

Because I thought (2m)^3 is 8m^3.

Answer 15

so we have then \[\sqrt{2m}^3*m\], no because the square root has the same priority as the power and is written first

Answer 16

what you say would be sqrt((2m)^3)

Answer 17

That's what I'm saying, sqrt((2m)^3).

Answer 18

and would be written this way \[\sqrt{(2m)^3}\]

Answer 19

Yup, that way

Answer 20

i thought you were supposed to be nice to people on this site? @SalvadorV

Answer 21

sorry, I didn't mean to be rude

Answer 22

so we have to simplify (2m)^-3=1/(2m)^3=1/8m^3 and we`d have \[\sqrt{\frac{ 1 }{ 8 }m^{-3}}*m\]

Answer 23

In that case, should it be -3 or 3?

Answer 24

and then we can take the sqrt as an exponent to simplify like \[\sqrt{\frac{ 1 }{ 8 }m ^{-3}}*m=\sqrt{\frac{ 1 }{ 8 }}*\sqrt{m ^{-3}}*m=\sqrt{\frac{ 1 }{ 8 }}*m ^{-3/2}*m\]

Answer 25

well,it's -3 in the first place right?

Answer 26

Yes, but if we do 1/((2m)^3). That's how you'd eventually get 1/8, right?

Answer 27

no, the 1/8 is because its -3, if it was 3 it would be 8m^3

Answer 28

Aah...yes, I see now.

Answer 29

what you do is make the (2m)^-3=1/2m^3

Answer 30

thats how you get it

Answer 31

do you want me to continue or do you need any further explaining?

Answer 32

I think I get it.

Answer 33

then you see I separate the 1/8 and the m^-3 because when you are making the sqrt of a product is the same as the product of the sqrts

Answer 34

\[\sqrt{ab}=\sqrt{a}*\sqrt{b}\]

Answer 35

Thanks for all the help!

Answer 36

heeey hold your horses, we haven't finished

Answer 37

we can still simplify one thing

Answer 38

*I mean the help, not all the help :). Yes, I know we're not done.

Answer 39

hahaha you're welcome C:

Answer 40

so, we have that \[\sqrt\frac{ 1 }{ 8 }*m ^{-3/2}*m\]

Answer 41

what happens when you multiply 2 values that have the same base but differnt exponents?

Answer 42

The exponents add up.

Answer 43

exactly, so we have\[m ^{-3/2}*m^1=m ^{(-3/2)+1}=m ^{1/2}\]

Answer 44

sorry, -1/2

Answer 45

and then we put it back to its sqrt form and simplify

Answer 46

\[\sqrt{\frac{ 1 }{ 8 }}*m ^{-1/2}=\sqrt{\frac{ 1 }{ 8 }}\sqrt{m ^{-1}}\]

Answer 47

here we use the same rule for the product of the sqrt as follows\[previous..thingy=\sqrt{\frac{ 1 }{ 8 }m ^{-1}}=\sqrt{\frac{ 1 }{ 8 }*\frac{ 1 }{ m }}=\sqrt{\frac{ 1 }{ 8m }}\]

Answer 48

Yes, and we can still simplify that, right?

Answer 49

Because 8m can be sqrt4 * 2m.

Answer 50

* sqrt2m

Answer 51

I don't think so.... how would you do that?

Answer 52

\[1/\sqrt{4}*\sqrt{2m}\]

Answer 53

By the way, the answer key says (sqrt2m)/4m as the answer.

Answer 54

well I guess but I don't believe that's simpler xD

Answer 55

I don't know how they get that final answer...

Answer 56

can you use the equation button to plug in exactly how it looks like?

Answer 57

\[\sqrt{2m}/4m\]

Answer 58

Sqrt2m is the numerator and 4m is the denominator.

Answer 59

okay, how does the first equation look, the one from which we started

Answer 60

Never mind, I figured it out.

Answer 61

okay