Question

can someone please help me with the rules for negative exponents
2^-2
(2)^-2
-2^2
(-2)^2 etc etc

Answer 1

Something raised to a negative exponent is the same as it's reciprocal raised to a positive exponent.

Answer 2

can u give me an example

Answer 3

2^-2=1/2^2

Answer 4

2^-2= (1/2) ^2

Those brackets are important if your numerator is not 1.

Answer 5

What about in this situation? For the function y=x^2, compute the average rate of change between x=-3 and x=3
average rate of change is:

Answer 6

Negative exponent really means to "inverse" the expression

Answer 7

For example, the inverse of \[2^{-2}\] is \[\frac{1}{2^2}\]

So it means to put 1 over the expression and remove the negative

Answer 8

Average rate of change is just slope

Answer 9

does that go for all numbers like 7^-13 would it be 1/7^13?

Answer 10

yes

Answer 11

yes, correct. The key to negative exponents is to realize that negative really means "inverse"

Answer 12

i noticed that when you plug in numbers for example: What about in this situation? For the function y=x^2, compute the average rate of change between x=-3 and x=3 average rate of change is:

Answer 13

As for finding the rate of change,

you first have to find the y values

Then create the points (x,y) and (x1,y1)

Then use the slope formula

Answer 14

it becomes a (-3)^2 rather than -3^2 why is that?

Answer 15

because you need to include the negative in the square

Answer 16

(-3)^2 means you are squaring -3 and the result will be positive
-3^2 means you are squaring the 3 and the result will still be negative

Answer 17

Once you find the y values, you will end up with points:

(3,9) and (-3,9)

When you calculate the slope (or the rate of change), you will realize that it is zero

Answer 18

@Hero, I don't like how you used "inverse" to describe a reciprocal. Inverse means something completely different in relation to functions.

Answer 19

replace inverse with reciprocal

Answer 20

What about in this situation? For the function y=x^2, compute the average rate of change between x=-6 and x=-3 average rate of change is:-9 but i came up with POSITIVE 9 can you explain why ? I put (-6)^2 and (-3)^2 which would equal to positive 36 and 9 respectively

Answer 21

(-6) - (-3) = -3

Answer 22

formula is f(x2) - f(x1)/x2-x1

Answer 23

so the -6 would not go first

Answer 24

it doesn't matter which goes first, they're interchangeable.

Answer 25

maybe I should have said Multiplicative Inverse

Answer 26

when i plugged in -3-(-6) it came out positive 3

Answer 27

Reciprocal = Multiplicative Inverse

Answer 28

if you plugged in your -3 as your first x, you would have to plug in your 9 as your first y

Answer 29

again, it doesn't matter which you plug in first, as long as the corresponding y is plugged in the same place.