why can't powers be negative??

Question

like 3 to the power of -2 is .111111111 not -9 (or so sead google)

Answer 1

Remember how powers are defined. 2^3 = 2*2*2. So, a nice feature of exponents is that multiplying numbers adds the exponents = for instance, 2^3*2^4 = (2*2*2)*(2*2*2*2) = 2^(3 + 4) = 2^7

Now, lets say you have the problem 2^7*2^x = 2^4. How would you solve this? By the nice exponent property above, this is the same as 7 + x = 4, so x = -3. But expanding these out, 2^7 = 128, 2^4 = 16, so 2^-3 should be 1/8.

This is also why anything (except 0) to the 0th power is 1:

a^x*a^0 = a^(x + 0) = a^x, so a^0 = 1

Answer 2

3 to the negative 2 is 1/9. 3 to the 2nd is 3*3. The negative means that it is in the denominator.

Answer 3

They can be negative, when the exponential expression is in the denominator.
Ex. 3 ^ (-2) = 1/ (3^2)
Note: Definition of Negative Exponents
If a is a nonzero real number and n is a positive integer, then
a ^(-n) = 1/(a^n)

Answer 4

I don't think you mean "why can't powers be negative", but rather "why can't the result of raising something to a power, be negative"?

well, it can

take (-3)^3 = -27, a negative number.

now if you specifically what that something raised to the power of 2, gives you a negative number, then you need to use Complex numbers.

the simplest Complex numbers would be an Imaginary number, such as 'i', which by definition, is the square root of 1.

so i^2=-1

complex numbers are typically part of studies of a bit more advanced math, typically done in college.

hope this helps a bit

Answer 5

if the power is negative, get the reciprocal of the base and make the exponent positive
in your example, 3 to the power of -2 is equal to 1 over 3 to the power of 2, or 1/9

Answer 6

3^-2 = 1/3^2=1/9=.1111111111111

Answer 7

Reverse the process..
The square root of -9 is 3i, where the i stands for imaginary number. This is a whole different number system.

Answer 8

by definition 3^-2 = 1/(3^2)
You can't argue with a definition.

Answer 9

Powers can be negative.