(-2x^{-2})^{3}(6x)^{2 }

______________

2(-3x^{-1})^{3}

hi,

can someone tell me how to do simplify that expression up there? ive been trying it for an hour to no avail.

this is from grade 11 functions, by the way.

thank you!

Guest Mar 28, 2017

#1**+1 **

(-2^{3}x^{-6})(36x^{2})/(2(-3^{3}x^{-3})=

(-8x^{-6})(36x^{2})/(-54x^{-3})=

(-8)(36x^{2})(x^{3})/-54x^{6=}

-288x^{5}/-54x^{6}=

-288/-54x=

16/3x

not totally sure. I wouldn't trust this to be right.

Guest Mar 28, 2017

edited by
Guest
Mar 28, 2017

#2**+3 **

First you could call this "distributing" the exponent, not sure what the real name is for this step.

\(\frac{(-2x^{-2})^3(6x)^2}{2(-3x^{-1})^3}=\frac{(-2^3x^{-2*3})(6^2x^2)}{2(-3^3x^{-1*3})}=\frac{(-8x^{-6})(36x^2)}{2(-27x^{-3})}\)

Now all terms with negative exponents in the numerator go to the denominator and lose the negative sign and vice versa.

\(\frac{(-8x^3)(36x^2)}{2x^6(-27)}\)

Now multiply the things in the numerator and the things in the denominator together.

\(\frac{-288x^{3+2}}{-54x^6}=\frac{-288x^{5}}{-54x^6}\)

Now reduce the fraction by 18x^{5}

\(\frac{-288x^{5}}{-54x^6}=\frac{16}{3x^{6-5}}=\frac{16}{3x}\)

Same as guest.

hectictar
Mar 28, 2017