What is the difference between (For example) (1)² and 1²? Or (1)-² and 1-²?

Question

unklerhaukus · Answer

$$x^{-1}=\frac 1x$$

$$x^{-n}=\frac1{x^n}$$

amistre64 · Answer

a negative exponent represents a reciprocal

anonymous · Answer

(disregard my last comment)

anonymous · Answer

$$(x)=x$$
Therefore$$1^2=(1)^{2}$$
$$1^{-2}=(1)^{-2}$$

unklerhaukus · Answer

$$(x)^m=x^m$$

$$(xy)^m=x^my^m$$

anonymous · Answer

$$1^{anything}=1$$

amistre64 · Answer

$$a^{(-n)} = \frac 1{a^n}$$

amistre64 · Answer

wow, did we all like post at the same time?  or is there something peculiar about the OS?

unklerhaukus · Answer

jam

unklerhaukus · Answer

knowledge jam

anonymous · Answer

Seems so

unklerhaukus · Answer

@KageWisdom do you still have questions?

anonymous · Answer

Haha. Thanks all. I sort of understand, but am still a bit confused, maybe I shouldn't have used 1 as my example coefficient. The negative exponents seem to be messing me up.

anonymous · Answer

So, yes, @UnkleRhaukus, I still have questions. If it turns into a fraction or a reciprical (I still don't understand that) then what's next? How would I solve 8 to the -3.

unklerhaukus · Answer

$$x^{-n}=\frac{1}{x^n}$$

$$7^{-2}=\frac{1}{7^2}=\frac 1{49}$$

anonymous · Answer

Ok, I think I understand now. I think I was doing where I multiplied 7*-7 instead of doing that. It's too early for algebra! :) Thank you guys so much!

unklerhaukus · Answer

what did you get for eight to the power of negative three?

anonymous · Answer

1/8 to the 3rd