power to negative

Question

Simple question... can't seem to figure this out.

2^-1=?
2^-2=?
2^-3=?
...
2^-n=?

jallenmorris · Answer

Do you undestand what a fraction in the exponent means ?

If you have  4^{\frac{1}{2}} = \frac{1}{sqrt{4}} = \frac{1}{2}

Similarly:

4^{-\frac{1}{2}} = 2  because  4^{-\frac{1}{2}}=\frac{1}{4^{\frac{1}{2}}}= \frac{1}{(\frac{1}{sqrt{4}})} = \frac{1}{(\frac{1}{2})} = 2

rahulgoyal1986 · Answer

4^(1/3) is the 3rd root (cube root) of 4.

4^-3 = 1/4^3 
4^-1/3 = 4^3

mgoblue123 · Answer

Thanks all. Had a hard time remembering the rules for negative powers.

hi0parag · Answer

As far as I know 
If you have  4^{\frac{1}{2}} = {sqrt{4}} = {2}

and as anything raised to negative power means inverse of the value with +ve power

4^{-\frac{1}{2}} = \frac{1}{sqrt{4}} = \frac{1}{2}  if x not equal to zero

Rules:
only one rule: x^(-y) =  1/(x^y)

judokan · Answer

2^-1=1/2=0.5
2^-2=1/4=0.25
2^-3=1/8=0.125
...
2^-n=1/(2^n)

Prep Toolkit