Rational exponents (was: Math Discussion)

[goolalklk]

Homework Statement

(-64)^(3/2)

Homework Equations

None.

The Attempt at a Solution

There is no answer that can be reached and it is supposed not be a real number. I was wondering why that is. How is it that there is no "real" answer to this problem?

 

[Mark44]

Homework Statement

(-64)^(3/2)

Homework Equations

None.

The Attempt at a Solution

There is no answer that can be reached and it is supposed not be a real number. I was wondering why that is. How is it that there is no "real" answer to this problem?

$(-64)^{3/2} = [(-64)^{1/2}]^3$
Does that answer your question?

 

[Eclair_de_XII]

Alternatively: (−64)^3/2 = √(-64)³

You're right in that there is no real solution. The square root of a negative number is an imaginary number, in which case you must use "i" to express √(-1).

i² = -1 and √(-1) = i.

 

[HallsofIvy]

When it says "there is no real solution to the problem" it means there is no real number. Do you understand the difference between "real numbers" and "imaginary numbers"?

 

[FeDeX_LaTeX]

There is no answer that can be reached and it is supposed not be a real number. I was wondering why that is. How is it that there is no "real" answer to this problem?

The negative sign makes it so that the stated number isn't real.

 

[SteamKing]

The negative sign makes it so that the stated number isn't real.

Not exactly.

Real numbers can be positive or negative. However, taking the square root of a negative number does not give a real number result. Instead, imaginary numbers were invented to overcome this problem. The imaginary unit i is defined such that i² = -1.