Mathematical Calculators

Exponent Calculator

This is an online calculator that can calculate exponents.

Exponent Calculator


Table of contents

What is an exponent?
Laws of Exponents

What is an exponent?

Exponentiation refers to a mathematical operation. It is written in as n. This involves the base and an exponent. n is a negative integer. Exponentiation refers to repeated multiplications of the base n.
a^n = a * a * ... * a n times
The calculator above can take negative bases but cannot calculate imaginary numbers. It cannot accept fractions. However, it can compute fractional exponents provided that the exponents are in their decimal form.

Laws of Exponents

These are the rules or laws that exponents must follow:
Multiplication with a joint base
According to the law, exponents with identical bases must be multiplied. Then exponents will be added together. In general:
ₐ ᵐ × ₐ ⁿ ₌ ₐ ₘ ₊ₙ ₐₙₔ ₍ₐ/₆₎ ᵐ × ₍ₐ/₆₎ ⁿ ₌ ₍ₐ/₆₎ ₘ ₊ ₙ
Dividing exponents using the same base
Subtraction of exponents is required when we divide exponential numbers with the same base. This law can be expressed in the following general forms:
₍ₐ₎ ₘ ÷ ₍ₐ₎ ₙ ₌ ₐ ₘ – ₙ
₍ₐ/₆₎ ₘ ÷ ₍ₐ/₆₎ ₙ ₌ ₍ₐ/₆₎ ₘ – ₙ
The law governing the power
This law states that we must multiply the powers if an exponential number is raised to another power. The general law is:
₍ₐ ₘ₎ ₙ ₌ ₐ ₘ ₓ ₙ
Multiplication of powers using different bases and the same exponents
The rule's general form is
₍ₐ₎ ₘ ₓ ₍₆₎ ₘ ₌ ₍ₐ₆₎ ₘ
The law on negative exponents
We can make an exponent negative by adding 1 to the numerator and the positive exponent to the denominator. This law can be referred to as:
ₐ ₋ₘ ₌ ₁/ₐ ₘ ₐ ₐₙₔ ₍ₐ/₆₎ ₋ₙ ₌ ₍₆/ₐ₎ ₙ
The law of exponent zero
If the exponent equals zero, then the result is 1. The basic form of the equation is:
ₐ ₀ ₌ ₁ ₐₙₔ ₍ₐ/₆₎ ₀ ₌ ₁
Fractional exponents
ₐ ₁/ₙ ₌ ₙ √ₐ

Parmis Kazemi
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Parmis Kazemi
Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things.

Exponent Calculator English
Published: Tue Dec 28 2021
In category Mathematical calculators
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