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Definition--Rationals and Radicals--Rational Exponent

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# Rational Exponent

## Topic

Rationals and Radicals

## Definition

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root.

## Description

Rational Exponents are a crucial concept in the study of Rational Numbers, Expressions, Equations, and Functions. These exponents are fractions, where the numerator indicates the power and the denominator indicates the root. For example, the expression

$$a^{m/n}$$

can be rewritten as

$$\sqrt[n]{a^m}$$

Understanding rational exponents is essential for simplifying expressions and solving equations involving exponents. They provide a bridge between radicals and exponents, allowing for more flexible manipulation of algebraic expressions. Rational exponents are widely used in various fields, including engineering, physics, and computer science, where exponential relationships are common. Mastery of rational exponents enables students to simplify complex expressions, solve equations, and apply these concepts to real-world problems. Rational exponents also play a significant role in calculus, where they are used in limits, derivatives, and integrals. By understanding rational exponents, students can better grasp the properties of numbers and their relationships, leading to a deeper comprehension of mathematical concepts.

For a complete collection of terms related to polynomials click on this link: __Rationals and Radicals Collection__

Common Core Standards | CCSS.MATH.CONTENT.HSA.REI.A.2, CCSS.MATH.CONTENT.HSN.RN.A.1, CCSS.MATH.CONTENT.HSF.IF.C.7 |
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Grade Range | 8 - 12 |

Curriculum Nodes |
Algebra• Rational Expressions and Functions• Rational Expressions |

Copyright Year | 2022 |

Keywords | radicals, radical expressions, rational numbers, rational expressions, definitions, glossary term, rational functions |