Question

How to simplify this monster?

Answer 1

LOL "monster" :D

Answer 2

\[\frac{ ( -16x ^{8}y ^{4}z ^{2})^{3}( -75x ^{5}y ^{7}z ^{9})^{4} (2y) ^{3} }{ ( 30x ^{10}y ^{9}z ^{8})^{3}( 40x ^{3}y ^{4}z ^{4})^{4} }\]

Answer 3

I could do everything...but I am sure there is a shorter way

Answer 4

keep in mind that, they're all factors

Answer 5

Oh....I will try :)

Answer 6

Thanks :) got it

Answer 7

yw

Answer 8

just as a check here is why I got:
\[ \frac{ ( -16x ^{8}y ^{4}z ^{2})^{3}( -75x ^{5}y ^{7}z ^{9})^{4} (2y) ^{3} }{ ( 30x ^{10}y ^{9}z ^{8})^{3}( 40x ^{3}y ^{4}z ^{4})^{4} }\]

\[ \frac{ ( -2^4x ^{8}y ^{4}z ^{2})^{3}( -3*5^2x ^{5}y ^{7}z ^{9})^{4} (2y) ^{3} }{ ( 2*3*5x ^{10}y ^{9}z ^{8})^{3}( 2^3*5x ^{3}y ^{4}z ^{4})^{4} }\]

\[ \frac{ ( -2^{12}x ^{24}y ^{12}z ^{6})( -3^4*5^8x ^{20}y ^{28}z ^{36})(2^3y^3)}{(2^3*3^3*5^3x^{30}y ^{27}z ^{24})(2^{12}*5^4x ^{12}y ^{16}z ^{16})}\]

\[ \frac{-2^{15}*3^4*5^8x^{44}y^{43}z^{42}}{2^{15}*3^3*5^7x^{42}y^{43}z^{40}}\]
\[ \frac{-\cancel{2^{15}}*3^{\cancel4}*5^{\cancel8}x^{2\cancel{44}}\cancel{y^{43}}z^{2\cancel{42}}}{\cancel{2^{15}}*\cancel{3^3}*\cancel{5^7}\cancel{x^{42}}\cancel{y^{43}}\cancel{z^{40}}}\]
\[ = -15x^2z^2 \]