SOLUTION: This is a practice GRE question, I'm confused as I think (X^#)^# should equal X^2# or X^# times X^#. For an answer they say the column A and B are equivalent. For all numbers x

Algebra ->  Exponents -> SOLUTION: This is a practice GRE question, I'm confused as I think (X^#)^# should equal X^2# or X^# times X^#. For an answer they say the column A and B are equivalent. For all numbers x      Log On


   

Question 887162: This is a practice GRE question, I'm confused as I think (X^#)^# should equal X^2# or X^# times X^#. For an answer they say the column A and B are equivalent.
For all numbers x, x^# = 24 - x.
Column A
( x^#)^#
Column B
x
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure what you're asking.  Apparently it's got something
to do with the laws of exponents.

Examples:  

%28X%5E3%29%5E4%22%22=%22%22X%5E12

X%5E3%2AX%5E4%22%22=%22%22X%5E7

Can you get it from those examples?  If not tell me about it in the
thank-you note form, and I'll get back to you.  It will help if you
can use letters instead of #'s.  Does the GRE guestion have #'s, and
do all the #'s refer to the same number or different numbers?

BTW, I just do this as a hobby, and I do not charge anybody any money,
ever.

Edwin

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
they are equivalent.

this is similar to:
if f(x) = x^2 + 1, then f(x-3) = (x-3)^2 + 1
you replace x with (x-3) in f(x) in order to get f(x-3) = (x-3)^2 + 1

this problem works the same way.

you have x^# = 24 - x

now they give you (x^#)^#
because x^# = 24 - x, this becomes:
(24-x)^#

now you have to replace x in the original function with (24 - x) and you will get:

(24-x)^# = 24 - (24-x) which becomes 24 - 24 + x which becomes x.

another way to look at it is to use another variable.

if x is any number, then y can also apply to the same logic because y can represent any number just as well as x can represent any number.

you get:

x^# = 24 - x
you also get an equivalent function of:
y^# = 24 - y

these functions are equivalent.
you just replaced x with y.
if x is 4 and y is 4, you'll get the same answer.

now start with (x^#)^#
since x^# = 24-x, that becomes (24-x)^#
now let y = (24-x) and you get:
(24-x)^# = y^#
now y^# = 24 - y, so your solution is 24 - y
but y = 24 - x, so your solution becomes 24 - (24 - x) which becomes 24 - 24 + x which becomes x.

this is a real mind warper but the basics of the problem is functional notation and how its used.

f(x) = 5x + 7
what is f(7)?
you replace x with 7 and your equation becomes f(7) = 5*7 + 7 .....

f(x) = x^2
what is f(x^2 + 3x - 2)?
you replace x with x^2 + 3x - 2 to get:
f(x^2 + 3x - 2) = (x^2 + 3x - 2)^2

it's the same concept even though you may not have seen it at first.