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HomeHomework HelpmathematicsWorking with Negative Powers

Working with Negative Powers

This topic covers the methods and principles for simplifying expressions involving negative powers, including the rules for removing negative indices and handling resulting fractions. It involves understanding the concept of equivalent expressions and applying exponent rules to simplify complex fractions. Mastering this topic is essential for working with algebraic expressions and equations in Mathematics.

intermediate
2 hours
Mathematics
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Overview

Working with negative powers is an essential concept in mathematics that helps us understand the reciprocal relationship of numbers. When a number is raised to a negative exponent, it signifies that we take the reciprocal of that number raised to the corresponding positive exponent. This concept is ...

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Key Terms

Exponent
A number that shows how many times to multiply the base by itself.

Example: In 2^3, 3 is the exponent.

Reciprocal
The inverse of a number, such that the product of a number and its reciprocal equals 1.

Example: The reciprocal of 5 is 1/5.

Negative Power
An exponent that is less than zero, indicating a reciprocal.

Example: x^(-2) = 1/(x^2).

Simplification
The process of reducing an expression to its simplest form.

Example: Simplifying 2^3/2^2 results in 2.

Base
The number that is raised to a power.

Example: In 3^4, 3 is the base.

Fraction
A part of a whole expressed as a ratio of two numbers.

Example: 1/2 is a fraction.

Related Topics

Exponents and Radicals
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Algebraic Expressions
Learn how to manipulate and simplify various algebraic expressions.
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Scientific Notation
Understand how to express large and small numbers using powers of ten.
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Key Concepts

ReciprocalExponent RulesSimplifying ExpressionsApplications in Science