How do you simplify #((2w^-4z^2)(-5z^-1))/(-4w^3)^-2#?

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Answer 1 · 2016-04-07T16:48:40

# +40zw^2#

Breaking this down into its component parts:

Write#" "2w^(-4)z^2" as "(2z^2)/w^4#
'...........................................

Write#" "-5z^(-1)" as "-5/z#

'...........................................

Write#" "(-4w^3)^(-2)" as " -1/(4w^6)#

so #1/((-4w^3)^(-2) ) = -4w^6#

'~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#(2z^2)/(w^4)xx(-5/z)xx(-4w^6)#

Giving:

#+ (2xx5xx4) xx (z^2xxw^6)/(zxxw^4)#

#40xxzxxw^2 = 40zw^2#