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How do you simplify #((5(r^-1)(s^-3)) / (3rs^2) ) ^ -2#?

Answer 1

Avery Alexander

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Answer 2

Kennedy Adams

To simplify ((5(r^-1)(s^-3)) / (3rs^2)) ^ -2, first, simplify the expression inside the parentheses. 5(r^-1)(s^-3) simplifies to 5/rs^3. The denominator 3rs^2 remains the same.

Now, combine the numerator and the denominator: 5/rs^3 / 3rs^2. To divide by a fraction, multiply by its reciprocal. The reciprocal of 3rs^2 is 1 / (3rs^2).

So, (5/rs^3 / 3rs^2) * (1 / (3rs^2)) = (5 / rs^3) * (1 / (3rs^2)) = 5 / (3r^2s^5).

Finally, raise the result to the power of -2: (5 / (3r^2s^5)) ^ -2 = (3r^2s^5 / 5) ^ 2 = (9r^4s^10) / 25.

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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.