- #1

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## Main Question or Discussion Point

I have been thinking on this topic for a while.

As I have seen on various sites:

1) a^(b/c) means "c"th root of "a^b".

2) Also an even root of a negative number does not exist in real numbers.

Then I want to investigate this formula:

a=(-4)^(1/2)

Mustn't it be equal to b=(-4)^(2/4)

However if we calculate the power first;

a=square root of [(-4)^1]= Not a real number

b=4th root of[(-4)^2]= 2

What do I miss? I have some confussion about decimal exponents but I hope the answer of this question will solve it.

As I have seen on various sites:

1) a^(b/c) means "c"th root of "a^b".

2) Also an even root of a negative number does not exist in real numbers.

Then I want to investigate this formula:

a=(-4)^(1/2)

Mustn't it be equal to b=(-4)^(2/4)

However if we calculate the power first;

a=square root of [(-4)^1]= Not a real number

b=4th root of[(-4)^2]= 2

What do I miss? I have some confussion about decimal exponents but I hope the answer of this question will solve it.