Basic rules for exponentiation If n is a positive integer and x is any real number, then xn corresponds to repeated multiplication xn = x × x × ⋯ × x ⏟ n times. We can call this “ x raised to the power of n,” “ x to the power of n,” or simply “ x to the n.” Here, x is the base and n is the exponent or the power.

For smaller exponents, we can multiply the base repeatedly by itself n times, where n represents the exponent. But for larger exponents, we use exponentiation by squaring or square-and-multiply algorithm to break down exponent into smaller parts.

Exponentiation is a mathematical operation, written as an, involving the base a and an exponent n. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times. a n = a × a ×... × a n times

If you wish to do exponentiation by hand, do the following: Determine the base and the power it's raised to, for example, 3⁵. Write the base the same number of times as the exponent. 3 3 3 3 3 Place a multiplication symbol between each base. 3 × 3 × 3 × 3 × 3. Multiply! 3 × 3 × 3 × 3 × 3 = 243.

This is the operation this online exponent calculator performs for you. When the exponent is a positive integer the operation is equal to multiplying the base by itself e times. If the exponent is a negative, for example -5, the operation is 1 divided by the base raised to the absolute value of the exponent: b-5 = 1 / b5.