Exponent Calculator

An exponent calculator is a mathematical tool that computes the result of raising a base number to a given power (exponent). This tool is essential for students, mathematicians, and professionals working with exponential functions, scientific notation, and various mathematical calculations involving powers.

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.

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 are a fundamental concept in arithmetic and algebra and are used in various mathematical operations and formulas, including exponentiation, logarithms, and scientific notation, to name a few.

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.