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How do you simplify #(36 m^4 n^3)/(24 m^2 n^5)#?

Answer 1

Eva Abramson

#=color(blue)(3/2 m^color(blue)(2) n^color(blue)(-2)#

#(36m^4n^3)/(24m^2n^5)#

#= (cancel36/cancel24) * (m^4n^3)/(m^2n^5)#

#=(3/2) (m^4n^3)/(m^2n^5)#

As per properties: #color(blue)(1/a=a^-1#

#color(blue)(a^m*a^n=a^(m+n)#

Applying the above properties to #m# and #n#

#=(3/2) m^4n^3 * m^color(blue)(-2)n^color(blue)(-5)#

#=(3/2) * m^color(blue)((4-2)) n^color(blue)((3-5))#

#=(3/2) * m^color(blue)((2)) n^color(blue)((-2))#

#=color(blue)(3/2 m^color(blue)(2) n^color(blue)(-2)#

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Answer 2

Kennedy Adams

To simplify the expression (36 m^4 n^3)/(24 m^2 n^5), you can divide the coefficients and subtract the exponents of the variables.

The simplified form is (3/2) * (m^4/m^2) * (n^3/n^5), which further simplifies to (3/2) * m^(4-2) * n^(3-5).

This simplifies to (3/2) * m^2 * n^(-2), or (3m^2)/(2n^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.