# Exponent Calculator

## What is an exponent?

An exponent, often referred to as a power or a superscript, is a mathematical notation used to indicate the number of times a base number should be multiplied by itself. It is a fundamental concept in mathematics and is typically expressed as a small number placed above and to the right of a base number. The base number is raised to the power of the exponent to calculate the result.

*a ^{n}* =

*a*×

*a*×

*...*×

*a*

In the expression "a^{n}," where "a" is the base and "n" is the exponent:

- The base (a) is the number that gets multiplied by itself.
- The exponent (n) tells you how many times the base should be multiplied by itself.

### For example:

- In 2
^{3}, the base is 2, and the exponent is 3. This means you multiply 2 by itself three times: 2 × 2 × 2 = 8. - In 5
^{2}, the base is 5, and the exponent is 2. This means you multiply 5 by itself two times: 5 × 5 = 25.

#### Exponents laws and rules:

- Product Rule:
- If you have two exponential terms with the same base being multiplied together, you can add their exponents:
- a
^{m}* a^{n}= a^{m + n} - For example: 2
^{3}* 2^{4}= 2^{3 + 4}= 2^{7}

- Quotient Rule:
- When you divide two exponential terms with the same base, you can subtract the exponent of the denominator from the exponent of the numerator:
- a
^{m}/ a^{n}= a^{m - n} - For example: 5
^{6}/ 5^{2}= 5^{6 - 2}= 5^{4}

- Power Rule:
- When you have an exponent raised to another exponent, you can multiply the exponents:
- (a
^{m})^{n}= a^{m * n} - For example: (3
^{2})^{3}= 3^{2 * 3}= 3^{6}

- Zero Exponent Rule:
- Any nonzero base raised to the power of zero is equal to 1:
- a
^{0}= 1 (for a ≠ 0) - For example: 7
^{0}= 1

- Negative Exponent Rule:
- If you have a nonzero base with a negative exponent, you can rewrite it as the reciprocal of the base raised to the positive exponent:
- a
^{-n}= 1 / a^{n} - For example: 2
^{-3}= 1 / 2^{3}= 1/8

- Exponent of 1 Rule:
- Any nonzero base raised to the power of 1 is equal to itself:
- a
^{1}= a - For example: 10
^{1}= 10

These basic exponent laws and rules are essential for simplifying and manipulating expressions involving exponents. They provide a foundation for more advanced algebraic operations and help solve a wide range of mathematical problems involving exponential notation.

See also