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How do you simplify #(5q^-2t^6)/(10q^2t^-4)#?

Answer 1

Savannah Anderson

#color(blue)(t^10/(2q^4)#

#(cancel5^color(blue)1q^-2t^6)/(cancel10^color(blue)2q^2t^-4)#

#:.=t^(6+4)/(2q^(2+2))#

#color(red)({t^6/t^-4=(t^6/1)/(1/t^4)=t^6/1 xx t^4/1=t^(6+4)=t^10}#

#color(red)({q^-2/q^2=(1/q^2)/((q^2)/1)=1/q^2 xx 1/q^2=1/q^(2+2)=1/q^4}#

#:.=color(blue)(t^10/(2q^4)#

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Answer 2

Genesis Allen

To simplify ( \frac{5q^{-2}t^6}{10q^2t^{-4}} ), first, simplify the coefficients: ( \frac{5}{10} = \frac{1}{2} ). Then, simplify the variables with the same bases by subtracting the exponents: ( q^{-2} \div q^2 = q^{-2-2} = q^{-4} ) and ( t^6 \div t^{-4} = t^{6-(-4)} = t^{10} ). Therefore, the simplified expression is ( \frac{1}{2}q^{-4}t^{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.