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How do you simplify #(12a^-9b^-4)/( 9a^2b^6)#?

Answer 1

Ethan Adkins

#=(4 a^-11 b^-10)/3#

#(12a^-9b^-4)/(9a^2b^6)#

#=(12/9) * ((a^-9b^-4)/(a^2b^6))#

#=(cancel12/cancel9) * ((a^-9b^-4)/(a^2b^6))#

#=(4/3) * (a^-9 / a^2 ) * ((b^-4)/(b^6))#

#=(4/3) * (a^(-9 -2) ) * (b^(-4 -6))#

#=(4/3) * ( a^-11) * (b^-10)#

#=4/3 a^-11 b^-10#

#=(4 a^-11 b^-10)/3#

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Answer 2

Jameson Allen

To simplify the expression (12a^-9b^-4)/(9a^2b^6), follow these steps:

Simplify the coefficients: 12/9 = 4/3
Combine the like terms in the numerator and denominator: a^(-9+2) = a^(-7), and b^(-4-6) = b^(-10)
Combine the simplified terms: (4/3) * (a^-7) * (b^-10)

Therefore, the simplified expression is (4/3) * (a^-7) * (b^-10).

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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.