Exponent Calculator

Online Exponent calculator helps you to find the exponent of any integer. Exponent refers to the multiplication of the same number at different times. Here, we have presented the exponent calculator which will provide you the result of the exponent with the detailed concept. Let's check and find the result of an exponent.

Exponents Calculator

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If a is any real number, successive multiplication of n as is an; that is, a x a x ... x a (n times a) an, where n is a positive integer. Here, n is index or power and a is base. Converse an — a x a x a x a .... (n times a). 

Exponents may not only be positive integers, they may be negative integers or positive fractions or negative fractions. That is, for base a belongs to R (set of real numbers) and power n belongs Q (set of rational numbers), an is defined. The case of n belongs to N (set of natural numbers) is especially considered. Besides, exponents may also be irrational. 

Basic rules of exponents

The basic rules of exponents are as follows:

1. If two exponential terms have the same base, then add the exponents.

For example:

$$3^4 \times 3^8 = 3^{4+8} = 3^{12}$$

2. If two exponential terms have different bases, then multiply the terms.

For example:

$$2^4 \times 3^8 = (2 \times 3)^{4+8} = 6^{12}$$

3. To divide exponential terms with the same base, subtract the exponents.

For example:

$$\frac{3^4}{3^8} = 3^{4-8} = 3^{-4}$$

4. To raise an exponential term to a power, multiply the exponents.

For example:

$$(3^4)^8 = 3^{4 \times 8} = 3^{32}$$

Properties of exponents

Some properties of exponents are:

• When two numbers with the same base are raised to the same exponent, the result is the same number raised to that exponent:

a^n = a^n

• When two numbers with the same base are raised to the same exponent, the result is the same number raised to that exponent:

a^n = a^n

• When a number is raised to the power of zero, the result is always one:

a^0 = 1

• When a number is raised to a negative exponent, the result is the reciprocal of the number raised to the positive exponent:

a^-n = 1/a^n

 

What is an exponent?

An exponent is a number that tells how many times a number is used as a factor.