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.

aⁿ = a×a×...×a

In the expression "aⁿ," 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 2³, the base is 2, and the exponent is 3. This means you multiply 2 by itself three times: 2 × 2 × 2 = 8.
• In 5², 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:

1. Product Rule:
   • If you have two exponential terms with the same base being multiplied together, you can add their exponents:
   • a^m * aⁿ = a^{m + n}
   • For example: 2³ * 2⁴ = 2^{3 + 4} = 2⁷
2. 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 / aⁿ = a^{m - n}
   • For example: 5⁶ / 5² = 5^{6 - 2} = 5⁴
3. Power Rule:
   • When you have an exponent raised to another exponent, you can multiply the exponents:
   • (a^m)ⁿ = a^{m * n}
   • For example: (3²)³ = 3^{2 * 3} = 3⁶
4. Zero Exponent Rule:
   • Any nonzero base raised to the power of zero is equal to 1:
   • a⁰ = 1 (for a ≠ 0)
   • For example: 7⁰ = 1
5. 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 / aⁿ
   • For example: 2^-3 = 1 / 2³ = 1/8
6. Exponent of 1 Rule:
   • Any nonzero base raised to the power of 1 is equal to itself:
   • a¹ = a
   • For example: 10¹ = 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.