- #1
Dickie
- 5
- 3
- Homework Statement
- Simplify [(-2t)^3] / [(-4t)^2] and evaluate (-2/3)^-2
- Relevant Equations
- 1/m^n = m^-n
I am able to simplify/evaluate the above equations correctly, however I end up with an incorrect sign for each answer (i.e positive when it should be negative) and I can't see where the error is. I feel I am clearly missing something but having checked my working including with a calculator for the basic arithmetic (to check the signs) I am none the wiser as to what I am actually getting wrong. Below are my workings:
= [(-2t)^3] / [(-4t)^2]
= [-8t^3] / [-16t^2]
= 1/2t
I am basing this on -8 / -16 = 1/2 and (t^3)/(t^2) = t, although the answer I am provided gives -1/2t which is leading to my confusion. I have also tried beginning with [(-2t)^3)] * [(-4t)^-2] giving [-8t^3] * [-1/16t^-2] however still end up with the same result.
= (-2/3)^-2
= (-2^1 * 3^-1)^-2
= (-2^-2 * 3^2)
= -1/4 * 9
= -9/4
However, again the answer provided is the opposite sign (in this case 9/4).
Looking back, my confusion is to do with a negative divided by a negative vs a negative fraction. So, if -(2/3) = (-2/3) = (-2/-3) [apologies, I can't think of a clearer way of explaining this] then I'd expect:
= -8 / -16
= -(8 / 16) = -8 / 16
= -1/2 which would give me the correct answer for the first question.
In that case I'd expect:
= (-2/3)
= -(2/3) = (-2 / -3)
So:
= (-2^1 * -3^-1)^-2
= -1/4 * -9
= 9/4
Is this then the correct logic I should be using?
= [(-2t)^3] / [(-4t)^2]
= [-8t^3] / [-16t^2]
= 1/2t
I am basing this on -8 / -16 = 1/2 and (t^3)/(t^2) = t, although the answer I am provided gives -1/2t which is leading to my confusion. I have also tried beginning with [(-2t)^3)] * [(-4t)^-2] giving [-8t^3] * [-1/16t^-2] however still end up with the same result.
= (-2/3)^-2
= (-2^1 * 3^-1)^-2
= (-2^-2 * 3^2)
= -1/4 * 9
= -9/4
However, again the answer provided is the opposite sign (in this case 9/4).
Looking back, my confusion is to do with a negative divided by a negative vs a negative fraction. So, if -(2/3) = (-2/3) = (-2/-3) [apologies, I can't think of a clearer way of explaining this] then I'd expect:
= -8 / -16
= -(8 / 16) = -8 / 16
= -1/2 which would give me the correct answer for the first question.
In that case I'd expect:
= (-2/3)
= -(2/3) = (-2 / -3)
So:
= (-2^1 * -3^-1)^-2
= -1/4 * -9
= 9/4
Is this then the correct logic I should be using?