How do I simplify the rational expression 2x^3y^-1 over 6(4x)^-2y^7 ?

Question

I am having the most difficulty with the 6(4x)^-2 part.
Please answer by 10:00 PM Pacific! Thanks in advance!

Answer 1

2x^3 y^-1 / 6(4x)^-2 y^7 remember the ^- needs to swich sides

2x^3 6(4x)^2 / 3y2y^7

2x^3 24x2 / 6y^9

48x^5 / 6y^9

8x^5 / y^9

Answer 2

Dont let a little negative exponent scare you. It works just the same as with a positive one. In fact, you can get it out of the denominator by multiplying both numerator and denominator by (4x)^2. Then you will have (32/6) x^5/y^8

Answer 3

so the problem looks like this
2(x^3)(y^-1)/6(4x)^-2y^7

so just move the 4x to the top and the y to the bottom so it looks like this

2*4^2x^(3+2)/6y^(1+7)
= 32x^5/6y^8
=16x^5/3y^8

Answer 4

observe distinction of squares in numerator and distinction of cubes in denominator. Now word the formula. (x - a million)(x + a million) ------------------- (a million - x)(a million + x + x^2) Now we element out -a million from denominator to make it seem as if numerator, and cancel. remember restriction of x != a million. (x - a million)(x + a million) ------------------- -a million(x - a million)(x^2 + x + a million) -a million (x + a million) --------------- x^2 + x + a million -x - a million --------- x^2 + x + a million