Ok : 2 to the power of -1 over 3 o the power -2?

Question

I dont want an exact answer i would like it in a form like this example: (-6) to the power of -1 = 1/6

Answer 1

2 to the power of -1 = 1/2
3 to the power of -2 = 1/9
Therefore, 2 to the power of -1 over 3 to the power -2 = (1/2) / (1/9) = 4.5

OR

2 to the power (-1/3 to the power 2) ==>
-1/3 to the power -2= (1/(1/3)) to the power of 2= 1 x (9/1)= 9
Therefore 2 to the power 9 = 512

OR

(2 to the power of -1/3) to the power of -2 = 2 to the power of 2/3 (following one of the laws of indices) = (cube root of 2) to the power of 2 = 1.59

So choose one

Answer 2

In effect, all you need to do is move the 2^-1 from the numerator to the denominator and flip the sign of the exponent. Similarly, move 3^-2 from the denominator to the numerator and flip the sign of its exponent. You end up with (3^2)/(2^1).

Here's why it works.

You start with (2^-1) divided by (3^-2).
That's (1/2) divided by (1/9).
Multiply numerator and denominator by 3^2, or 9.
Then you get (2^-1)*(3^2) divided by (3^-2)*(3^2)
That's (1/2)*9 divided by (1/9)*9
Or simply (1/2)*9 divided by 1.

Then multiply numerator and denominator by 2^1.
That's (2^1)*(2^-1)*9 divided by 1*(2^1)
Which simply ends up being 9/2, or four and a half.

Hopefully that helps!

Answer 3

it will be 3 to the power of to, over 2 to the poer of 1, it will be 9/2 = 4.5

Answer 4

((2 ^ -1)/3) ^ -2

2 ^ -1 is 1/2

1/2 divided by 3 is 1/6

1/6 ^ -2 is 6 ^ 2 ie 6 squared which is 36.

Answer 5

(1/2) / (1/9) = (1/2) x (9/1)
= (9/2)
= 4 & (1/2) or 4.5

Answer 6

x^-n = 1/x^n

1/x^-n = x^n