#1**-2 **

They are the same, because if a whole-number base has its reciprocal as a exponenet, the answer is always one.

CalculatorUser
Oct 27, 2018

#2**0 **

They are all the same, but if you take a number's reciprocal and square it by the number, and the number is a power of 2, you get the square root of 2, NOT 1. This is because when you simplify the other equations, you get the square root of 2, every single time under these conditions. Remember, fractions as exponents are square roots to the power of the reciprocal of the fraction. Therefore they are all the same. Around 1.41421356237 ish, but the decimal never ends.

-MathCuber

MathCuber
Oct 27, 2018

#4**+2 **

I think this is what your teacher would want you to do

which is smallest:

2^(1/2), 4^(1/4), 8^(1/8)

\(2^{\frac{1}{2}}\\~\\ 4^{\frac{1}{4}} = 2^{2\cdot\frac{1}{4}} = 2^{\frac{1}{2}}\\~\\ 8^{\frac{1}{8}}=2^{3\cdot\frac{1}{8}}=2^{\frac{3}{8}}\\~\\ \)

3/8 is smaller than 1/2 so it will be the smallest one.

Melody
Oct 27, 2018