# The Square Roots of the Powers of 2

## There's something special about the square roots of the powers of 2, if you look closely...

Have you noticed what's special about the square roots when **2** is raised to an *odd* exponent? When **2** is raised to an *even* exponent, the square root of the power is equal to **2 ***to the power of the exponent's half!* But when **2** is raised to an *odd* exponent, the square root of the power is equal to *a multiple of the square root of *2! In fact, it'll be **2 ***to the half of the previous even exponent multiplied by the square root of *2!

## Another important fact to remember about square roots is that:

## X^½ = the square root of X

The **caret** (^) is the symbol of exponentiation. Raising a number to the power of ½ gives you the square root.

## What if you raise 2 to a *negative* exponent, you ask? Simple! That'll just give you the *reciprocals* of the *positive* powers!

### P.S.: Raising 2 to the power of an imaginary or complex number will give you a random complex number & the square roots of such numbers are also complex. So this math trick will only work with real numbers. Pick real integers as exponents only. And remember: 2 must be the base!

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© Derek Cumberbatch