In mathematics, the operation of repeated multiplication is called exponentiation. This is an extension to the operation of multiplication in the same way that multiplication is an extension to the operation of addition when the same number is added repeatedly. For example,
Here, 2 is the base, 5 is the exponent, and 32 is 2 raised to the 5th power or 2 raised to the power 5. The base 2 appears 5 times in the repeated multiplication, because the exponent is 5. Unlike multiplication, exponentiation is not commutative:2×5 = 2+2+2+2+2 = 10 repeated addition 25 = 2×2×2×2×2 = 32 repeated multiplication
Also, exponentiation is not associative:23 = 8 32 = 9
When the exponent is 1, it is not usually given. The exponents 2 and 3 occur frequently; they are often given as the square and cube of the base, respectively. For example, 52 is five squared, and 43 is four cubed.(23)4 = 84 = 4,096, 2(34) = 281 = 2,417,851,639,229,258,349,412,352
4.1. Integer exponents
4.2. Rational exponents and radicals
4.3 Complex roots of real numbers
4.3.1. Polar Form of Complex Numbers
4.3.2. DeMoivre’s Theorem
4.4. Irrational exponents
4.5. Complex exponents
4.6. Scientific notation
4.7. Squaring algorithm
4.8. Solved problems