restricting the domain of (5a^2b)^2/5

[dayton1]

Ok I hope I write this out correctly:

One of the expressions below is almost equivalent to (5a^2b)^2/5 and would be the same if we restrict the domain slightly, identify which one and explain why:

a). 5^2/5 a^1/5 b^2/5
b). square root of (5a^2 b)^5
c). 2a^4/5 b^2/5
d). (5^2/5 b^2/5)/(a^-4/5).

I am not sure how to begin this...I don't know what he means by restrict the domain slightly...any help? Thanks!

 

[arthur ohlsten]

[5a^2b]^2/5
5^2/5 [a^2]^2/5 b^2/5
[5^2/5] [a^4/5] b^2/5
[5^2/5] [b^2/5] / a^(-4/5) this is identical to d

d and the original should have the identical domain.

I don't know what is meant by " they would be the same with a slight restriction to the domain"

Arthur

 

[stapel]

I don't know what is meant by " they would be the same with a slight restriction to the domain"

In the original expression, "a" could equal zero. I don't think this would be allowed, once "a" is in the denominator. :idea:

Eliz.

 

[dayton1]

Hmmm, I'm still not sure if I get it. I don't understand how you simplify (5a^2 b)^2/5 to get:

[5^2/5][b^2/5 / a^(-4/5)

 

[dayton1]

I understand how you would get [5^2/5] [a^4/5] [b^2/5]...but how does the a^4/5 become negative and end up as the denominator?????

 

[arthur ohlsten]

let us examine 1/100
this is the same as 1/10^2
this is the same as 10^-2

10^2=100
10^1=10
10^0=1
10^-1=1/10
10^-2=1/100

if you have a term in the numerator and which to place it in the denominator just change the sign of the exponent, and move it.

10^2multiply by 10^-2/10^-2
[10^2][10^-2] / 10^-2
1/10^-2

or 10^2 is identical to 1/10^-2

Arthur

 

[dayton1]

Thanks so much for your help! I get it now. For some reason I was blanking on that rule :roll: