The Powers of Terrific Two!

2⁷ + 2⁷ = 2⁸ (2⁷ = 128; 128 + 128 = 256; log₂256 = 8)

2¹⁰ + 2¹⁰ = 2¹¹ (2¹⁰ = 1,024; 1,024 + 1,024 = 2,048; log₂2,048 = 11)

2²⁴ + 2²⁴ = 2²⁵ (2²⁴ = 16,777,216; 16,777,216 + 16,777,216 = 33,554,432; log₂33,554,432 = 25)

2^½ + 2^½ = 2^3/2 (2^½ = 1.4142...(the square root of 2); the square root of 2 doubled is the square root of 8; log₂2.8284...(the square root of 8)= 3/2 or 1½)

2^-1 + 2^-1 = 2⁰ (2^-1 = ½; ½ + ½ = 1; log₂1 = 0)

2^-2 + 2^-2 = 2^-1 (2^-2 = ¼; ¼ + ¼ = ½; log₂½ = -1)

As you can see, even if x is a non-integer or negative, it still works out! Even imaginary/complex powers work out in this math trick!

2ⁱ + 2ⁱ = 2¹⁺ⁱ (This statement is true but 2ⁱ & 2¹⁺ⁱ are both equal to irrational complex numbers, so I would have to type too many random digits!)

If you have a graphing calculator that can work with imaginary numbers, then you can see what those irrational complex numbers are.

The Powers of Terrific Two!

2^x + 2^x = 2^x+1

It doesn't matter what number x is!

Examples:

Also, don't forget that if you multiply 2 factors with exponents of the same base, then the exponents will add up!

2^x × 2¹ = 2^x+1 & 2^x + 2^x = 2^x × 2; also, x + x = 2x

So it figures why this math trick works! And also remember that:

y¹ = y

No matter what y is!

The Powers of Terrific Two!

2x + 2x = 2x+1

It doesn't matter what number x is!

Examples:

Also, don't forget that if you multiply 2 factors with exponents of the same base, then the exponents will add up!

2x × 21 = 2x+1 & 2x + 2x = 2x × 2; also, x + x = 2x

So it figures why this math trick works! And also remember that:

y1 = y

No matter what y is!

2^x + 2^x = 2^x+1

2^x × 2¹ = 2^x+1 & 2^x + 2^x = 2^x × 2; also, x + x = 2x

y¹ = y