How do you evaluate #(- 5u ^ { 2} z ^ { 4} + 4u z ^ { 3} ) \div ( - 2u ^ { 2} z ^ { 4} )#?

1 Answer
Jim G.
Sep 17, 2017

#5/2-2/(uz)#

Explanation:

#"using the "color(blue)"law of exponents"#

#•color(white)(x)a^m/a^n=1/a^((n-m))to(n>m)#

#"divide each term on the numerator by "(-2u^2z^4)#

#rArr(-5u^2z^4)/(-2u^2z^4)+(4uz^3)/(-2u^2z^4)#

#"separate the factors into a product"#

#rArr-5/2xxu^2/u^2xxz^4/z^4+4/(-2)xxu/u^2xxz^3/z^4#

#color(blue)"cancel ""common factors on numerator/denominator"#

#=5/2xxcancel(u^2)^1/cancel(u^2)^1xxcancel(z^4)^1/cancel(z^4)^1-cancel(4)^2/cancel(2)^1xxu/u^2xxz^3/z^4#

#=5/2-2/1xx1/u^((2-1))xx1/z^((4-3))#

#=5/2-2/1xx1/uxx1/z#

#=5/2-2/(uz)#

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