For any nonzero real numbers a and b and any integers m and t, how do you simplify #(-a^m/b^t)^(2t)#?

Answer 1

See a solution process below:

We can use this rule of exponents to simplify the expression"

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(-a^color(red)(m)/b^color(red)(t))^color(blue)(2t) => (-a)^(color(red)(m) xx color(blue)(2t))/(b)^(color(red)(t) xx color(blue)(2t)) => (-a)^(2mt)/(b)^(2t^2)#

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Answer 2

Eli Assouline

To simplify ((-a^m/b^t)^{2t}), you raise the numerator and denominator to the power of (2t), resulting in ((a^m)^{2t}/(b^t)^{2t}). Then, simplify the exponents, giving (a^{2mt}/b^{2t^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.