Simplifying Expression?

Question

13^4 / √(13^10)

Do you simplify it like this:

13^4 / √(13^10)
13^4 / 13^5 (after √(13^10) = (13^10)^(1/2) = 13^5)
1/13

Or like this?:

13^4 / √(13^10)
(13^4)^2 / (√(13^10))^2 (square the numerator and denom.)
13^8 / 13^10
1/(13^2)
1/169

Which is correct?

Answer 1

13^4 / √(13^10)
13^4 / 13^5 (after √(13^10) = (13^10)^(1/2) = 13^5)
1/13
is the correct way.

You could also do it in the following way:
13^4 / √(13^10)
√[(13^4)^2 / (√(13^10))^2]
√[13^8 / 13^10]
√[1/(13^2)]
1/13

Answer 2

division is subtraction of a common base number
x^3/x^1 = X^2 ... 3-1=2
x^5/x^1 = X^4 ... 5-1=4
etc...


-------------- THIS SECTION IS WRONG see below for more info------------
sq is division
so
√(x^10) ... 10-2 = 8
is x^8

^5 √(x^10) ... 10-5 =5
=x^5 <----(I'm remembering exponent - root = either root or exponent if negative root remaining if positive exponent remaining.. I COULD BE OFF ON THIS) I'm remembering that it is cancelation... of the two values that is root value offsets the exponent value.. but I'm remembering something about division as well.. I think that is the inversion or reciprocal portion explained above for non single term reductions


--------------END OF THE REALLY WRONG section see below for more info------------

you can work it out by actually checking the math following bedmas

lets sub 2 instead of 13
2^4 / √(2^10)
16 / √1024
16 / 32
= 1/2 (where 2 = x) (if x=13 then it would be 1/13)

I could have my math off

1/13 or
1/169

if you are left with

x^4 / x^5

you get
x^-1

if x = 13

then you have
13^-1

or 1/13th

anyway.. I could have did math wrong I'm not a mathie

hope it helps

--------- THE SECOND REALLY WRONG!!!! SECTION for final solution see below - after you....----------
13^4 / √(13^10)

then x^4 / √(x^10) 10-2 = 8
then x^4 / x^8 4-8= -4
x^-4

where x = 13

13^-4
13^(-4) = 3.50127797 × 10-5 ?????
1 / 169 = 0.00591715976
obviouslly I must be doing something wrong as I don't think either is correct


hmm.

--------- END OF THE SECOND REALLY WRONG!!!! SECTION for final solution see below - after you....----------

OK NOW I GOT IT GUY UP A FEW WAS RIGHT..
see: Fractional or Rational Exponents on http://oakroadsystems.com/math/expolaws.htm


SO

13^4 / √(13^10)
13^4 / 13^10/2 (simplify)
13^4 / 13^5 ... 4-5=-1 (simplify)
13^-1 (invert)
= 1/13

Answer 3

1/13.

Answer 4

1/13 is correct.

You don't square both the numerator and denominator, then try to solve. That's just like saying 5/9 = 25/81, which of course is not true.

Answer 5

The first is correct. Squaring the num and denom changes the value of the fraction. I know what you were thinking, to get rid of the radical. But to do that, you'd multiply both the num and denom by the denom, not square them both. If you multiply top and bottom by the denom, you'll get 1/13, same as your first answer.

Answer 6

The first way.

The problem is that you can't square the top and bottom:

1/2 => 1^2/2^2 = 1/4. That clearly isn't right.

Best.