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WEEK 7-EXPLORING-RATIONAL-EXPONENTS

VIMSCHOOL

Created on July 20, 2024

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Transcript

Exploring Rational Exponents

Objectives

Start

Laws of Exponents

Story

From Radicals to Rationals

Evaluating Expressions

Summary

Laws of Exponents

Properties of Exponents

Let a,b be real numbers and n,m be integer numbers, the following properties holds:

aᵐaⁿ = aᵐ⁺ⁿ
1 aᵐ
= a⁻ᵐ
(aᵐ)ⁿ = aᵐⁿ

Properties of Exponents

a⁰=1
(ab)ᵐ = aᵐbᵐ
aᵐaⁿ
=aᵐ⁻ⁿ

Click here to draw >

Match the property used to simplify the expression

  • aᵐaⁿ = aᵐ⁺ⁿ 2¹⁰×2¹²=2²²
  • 1 /aᵐ= a⁻ᵐ 3⁻³=1/27
  • (aᵐ)ⁿ = aᵐⁿ (x⁻³)²=x⁻⁶
  • aᵐ/aⁿ=aᵐ÷ⁿ 3⁴/3⁶=3⁻²

The solution will appear in 30 seconds

aᵐaⁿ = aᵐ⁺ⁿ

2¹⁰×2¹²=2²²

1 /aᵐ= a⁻ᵐ

(x⁻³)²=x⁻⁶

(aᵐ)ⁿ = aᵐⁿ

3⁴/3⁶=3⁻²

aᵐ/aⁿ=aᵐ÷ⁿ

3⁻³=1/27

In addition, there are some properties for rational exponents and radicals.

But before moving on, let's define rational exponents.

Story

From Radicals to Rationals

Rational Exponent as a Radical

Definition: Let a ∊ℝ, n ∊ℤ and the expression . Then:

Example 1: Let a=4 and n=2, then:

Properties of Radicals & Rational Exps.

Let a,b be real numbers and n,m be integer numbers, the following properties holds:

Properties of Rational Exponents & Radicals

Evaluating Expressions

Let's see some examples:

Example 2: Evaluate the expression

Example 1: Find the value of the expresssion

1/16

Let's see some examples:

Example 4: Simplify (x⁤≥0):

Example 3: Expand as a radical expression

x/4

Try it by yourself:

Summary: Properties of Rational Exponents & Radicals

As a Rational Exponent

As a Radical

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

9TH-EXPLORING-RATIONAL-EXPONENTS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

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MA.912.NSO.1 Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms. MA.912.NSO.1.1 Extend previous understanding of the Laws of Exponents to include rational exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions involving rational exponents. MA.912.NSO.1.2 Generate equivalent algebraic expressions using the properties of exponents.

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MATERIAL

It is highly advised to have:

  • Grid paper.
  • Pencils of different colors.
  • Eraser.
  • A rule.
  • A calculator.
  • Geogebra installed on your phone/tablet/computer (or use online version).