Exponents Calculator

Instructions:

• Enter the base and exponent values.
• Check the "Calculate Square Root" box if you want to calculate the square root.
• Click the "Calculate" button to perform the calculation.
• The result will be displayed along with the detailed explanation and formula used.
• Your calculation history will be listed below.
• Click the "Clear" button to clear the input fields and result.
• Click the "Copy" button to copy the result to the clipboard.

Base:

Exponent:

Result:

Calculate Square Root

Calculate Clear CopyCalculation Details:

Calculation History:

The Exponents Calculator is a tool that helps to calculate the value of a number raised to a power. It is a simple and easy-to-use tool that can be used to simplify expressions, solve equations, and find roots of polynomials.

Concepts

Exponents

An exponent is a mathematical operation that indicates the number of times a number is multiplied by itself. For example, 2^3 means 2 is multiplied by itself 3 times, which is equal to 2 × 2 × 2 = 8.

Powers

A power is the result of raising a number to an exponent. For example, 2^3 = 8, where 2 is the base and 3 is the exponent.

Laws of Exponents

The laws of exponents are a set of rules that govern the manipulation of exponents. These laws are used to simplify expressions, solve equations, and find roots of polynomials. The basic laws of exponents are:

• Product Law: a^m × a^n = a^(m+n)
• Quotient Law: a^m / a^n = a^(m-n)
• Power Law: (a^m)n = a^(mn)
• Negative Exponent Law: a^-m = 1/a^m
• Zero Exponent Law: a^0 = 1

Scientific Notation

Scientific notation is a way of expressing numbers that are very large or very small. It is a shorthand way of writing numbers using powers of 10. For example, the number 300,000,000 can be written as 3 × 10^8 in scientific notation.

Formulae

The formula for calculating the value of a number raised to a power is as follows:

a^n = a × a × a × … × a (n times)

Benefits

The Exponents Calculator has several benefits, including:

• It simplifies expressions.
• It solves equations.
• It finds roots of polynomials.
• It saves time and effort.

Interesting Facts

• The number e, which is approximately equal to 2.71828, is a special number in mathematics that is used in many areas of science and engineering. It is the base of the natural logarithm function.
• The number 2^64 is approximately equal to 18.4 quintillion, which is a very large number.
• The number 2^-64 is approximately equal to 5.42101 × 10^-20, which is a very small number.

References

• Weisstein, Eric W. “Exponent.” From MathWorld–A Wolfram Web Resource¹.
• Sloane, N. J. A. Sequence A001348 /M2930 in “The On-Line Encyclopedia of Integer Sequences.” ¹.
• OpenStax. “1.2 Exponents and Scientific Notation.” ².