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How do you simplify #((r^-1s^2t^-3)/(r^-2s^0t^1))^-1#?

Answer 1

Kennedy Adams

#r^-1s^-2 t^4# or #t^4/(rs^2)#

First, you can remove the denominator of this equation by applying the exponents rules as follows:

#((r^-1s^2t^-3)/(r^-2s^0t^1))^-1 -> (r^(-1 - -2) s^(2 - 0)t^(-3 - 1))^-1 ->#

#(r^(-1 + 2) s^2t^-4)^-1 -> (r^1s^2t^-4)^-1#

Using the exponent rules, we can now apply the exponent to the entire term after simplifying the fraction.

#(r^1s^2t^-4)^-1 -> r^(1*-1)s^(2*-1)t^(-4*-1) -> r^-1s^-2 t^4# or

#t^4/(r^1s^2) -> t^4/(rs^2)#

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Answer 2

Abigail Allen

To simplify ((r^-1s^2t^-3)/(r^-2s^0t^1))^-1, first apply the negative exponent to invert the expression:

= ((r^2s^-2t^3)/(r^1s^0t^-1))

Next, simplify each term:

= (r^(2-1)s^(2-0)t^(3-(-1)))

= (r^1s^2t^4)

= rst^4

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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.