Question

Simplify using only positive exponents.

(2r^-1s^2t^0)^-2
----------------
2rs

Thanks in advance!

Working this out:

(2^-2 r^2 s^-4)/ (2 r s) =

r^2/8rs^5

Note: Anything to the 0 power is equal to 1.

I hope this will help.


Sorry but can you help me please I seriously need it.!

how did you get
(2^-2 r^2 s^-4)?

For the numerator (top) we have:
(2 r^-1 s^2 t^0)^-2

Multiply the exponents for each term. For example, (r^-1)^-2 is r^2 --> -1 * -2 = 2

Therefore you have: (2^-2 r^2 s^-4 t^0) or just (2^-2 r^2 s^-4) because t^0 is the same as 1.

I hope this is clearer and will help.

Don't you add the exponents when you are multiplying?

i agree..... anything to the power of 0 is 1

Check your rules for exponents when determining how to treat them.

If you have something like this:
r^2 * r^3 -->with the same base, you add the exponents. This would be r^5 (I'm using * to mean multiply.)

If you have something like this:
(r^2)^3 -->with the same base, you multiply the exponents. This would be r^6 because this is a different rule.

I hope this will be a little clearer.

Oh, thank you!

wait, but then how do you get

r^2/8rs^5 as the answer?

where in the world did the 8 come from?

Check out negative exponents to determine how to treat them. If you have a negative exponent in the numerator (top), flip to the denominator (bottom) and make the exponent positive. If you have a negative exponent in the denominator, flip to the numerator and make the exponent positive.

We had this:
(2^-2 r^2 s^-4)/ (2 r s)

Flip the negative exponents (with their respective bases) to the denominator and make them positive.

I'll show you what I mean:

r^2 / (2^2 s^4 2 r s) -->flipping 2^-2 to the denominator and making the exponent positive AND flipping s^-4 to the denominator and making the exponent positive. (Note: 2^2 = 4)

Simplifying:

r^2 / (4 s^4 2 r s) -->multiply 4 * 2 to get 8; add exponents with the same bases. s^4 * s gives us s^5

We end up with:
r^2 / 8rs^5

I hope this helps.

Wow, thanks!