Help with 2 algebra problems (with exponents and roots)

[ElectroNewby]

I've done many of those algebra problems lately but I just cannot make any sens of these two... tried many times but I never come up close to the red answer for the problem #2. With problem #1 I'm pretty sure I'm not far off but it's the only problem with "a+b" exponents instead of numbers and I'm lost! With problem two well I would just flip the roots and use the number as denominators for the exponants but I dunno how they arrive at 8root(x/y).

My answer for #1 is x^4a+4b/y^8b+2a
;(

I need some help, I really want 100% in my exam but these two bad boys are frustrating (for now)

thanks 1000 times!!

 

[jpanhalt]

Try expanding each term to have only a single exponent, e.g.,X^(a+b) becomes (X^a)(X^b) and so forth.

John

PS: Sorry for the absence of Latex. The new editor didn't work the way I expected, and my crib sheet is at another location.

 

[Ratchit]

I've done many of those algebra problems lately but I just cannot make any sens of these two... tried many times but I never come up close to the red answer for the problem #2. With problem #1 I'm pretty sure I'm not far off but it's the only problem with "a+b" exponents instead of numbers and I'm lost! With problem two well I would just flip the roots and use the number as denominators for the exponants but I dunno how they arrive at 8root(x/y).

My answer for #1 is x^4a+4b/y^8b+2a
;(

I need some help, I really want 100% in my exam but these two bad boys are frustrating (for now)

thanks 1000 times!!

View attachment 80837

ElectroNewby,

Lots of folks including mathematicians say that mathematics is a "language". I have thought long and hard about that concept, but I don't agree with it. Here is why. It cannot describe quantities that a "real" language can; like desire, greed, anger, fustration, and a thousand other emotions. Mathematics is nothing unless is it supported by a language that defines the quantities it manipulates. It is like shorthand, which is meaningless without a social language to work on. I consider mathematics as a method, a sophisticated bookkeeping method. As in any bookkeeping method, what is done on one entry is balanced in another entry. In the solution to the first problem, powers are lowered, exponents are computed, and the expression is raised the same amount it was lowered to maintain the balance. In the second problem the expression is raised to the 6th power, the exponents and coefficient calculated, and the 6th root is calculated for the answer.

Ratch

 

[ElectroNewby]

Awesome,
thank you so much for your time and help.
I'm doing it again on paper to make sense of it all!

still unsure why the first one becomes x(a+b)-(a-b) but I'll find out!

edit: ahhh how unaware am I ... you bring the exponent up but don't change the sign in the parenthesis, but of course gets subtracted because of the exponent laws with a division

You cleared the mud in my eyes ^^