Exponent Calculator

What is an Exponent?

Exponent is used in the exponentiation expression, which tells how many times a number (base) is multiplied by itself. Exponent is written at the upper right-hand corner of the base and mathematically represented as “aⁿ or bⁿ”.

In this exponentiation expression “a & b” are known as the base and “n” is known as the exponent or power. This “n” power is positive or negative and works as a deciding factor to repeat the multiplication of the base for the respective exponent.

For example:

• If the exponent of 5 is 3 then 5³ = 5 × 5 × 5 = 125.
• “x²”means it multiplies two times such as: x × x and 4² = 4 × 4 = 16.

Laws of Exponents

Before the solution of any exponentiation expression you have to be familiar with basic exponent laws & rules:

• If the two numbers are multiplied together with the same base but different exponents then it is solved by adding the exponent such as: aⁿ × a^m= a^(n+m).
• If the exponent is negative then it can removed by reciprocating the base and raising the exponent with a positive sign. i.e., a^(-n)= 1/aⁿ.
• If exponents of any base are raised to another exponent, then exponents are multiplied together. i.e., (a^m)ⁿ= a^{(m × n)}.
• When two bases are raised by a single power then power is distributed on both bases such as: (a × b)ⁿ= aⁿ × bⁿ & (a/b)ⁿ = aⁿ/bⁿ.
• If the value of exponent is 1 then it returns the same base. i.e., a¹= a.
• If the exponent of any base is “0” then its value is always “1” (i.e., a⁰= 1). Moreover, “0⁰” is undefined, sometimes conventionally taken as 1.

How to Solve Exponents?

For quick solutions of exponentiation expression use the exponents calculator. However, if you want to solve it by hand then do so by the below steps:

• Note the base & exponent from the given expression.
• Now, write the base number of times as the exponent indicates with a multiplication sign. i.e., 3⁵=3 × 3 × 3 × 3 × 3.

1. 1. 1. If “n” is positive: aⁿ= a × a × ... × a (n times)
      2. If “n” is negative: a^-n= (1/a)ⁿ = (1/a) × (1/a) × (1/a) ×… × (1/a) (n times)

• Finally, multiply all repeated bases and get the final exponent value. i.e., 3 × 3 × 3 × 3 × 3 = 243.

With these steps, calculating the exponent value for small numbers is easy. But it is quite difficult if the exponent & base is a large number, decimals, or negative. To remove this difficulty use our base calculator and get accurate results for any base or exponent.

Example:

Find a value of 2 to the power of 5.

The 2 raised to the power 5 is written as: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.

What is 3 to the power of 2?

The “3 to the power of 2 is “9” and mathematically written as: 3² = 3 × 3 = 9.

Find the value of “-3 raised to the power of 3”.

It is written as: (-3)³ = -3 × -3 × -3 = -27.

Important Exponents Values

Here we provided some important results of exponentiation expressions for positive, negative, and decimal exponents by using the above exponential calculator.