6-3: Rational Exponents Unit 6: Rational /Radical Equations.

Slides:



Advertisements
Similar presentations
Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.
Advertisements

1 How Do We Use Rational Exponents? Do Now: Perform the indicated operation and simplify 1. 2.
7. Roots and Radical Expressions
Ch 8 - Rational & Radical Functions Simplifying Radical Expressions.
Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.
Review: Laws of Exponents Questions Q: 4 0 =? A: 1 Q: 4 1 =? A: 4 Q: 4 1/2 =? A: Let’s square the number (4 1/2 ) 2 =? (4 1/2 ) 2 = 4 1 = 4 Recall: b.
5.7 Rational Exponents Fraction Exponents.
Algebra 2 Bellwork – 3/4/15.
10.2 Rational Exponents.
7.1/7.2 Nth Roots and Rational Exponents
6.1 n th Roots and Rational Exponents What you should learn: Goal1 Goal2 Evaluate nth roots of real numbers using both radical notation and rational exponent.
Radical Functions & Rational Exponents
7.1 nth Roots and Rational Exponents 3/1/2013. n th Root Ex. 3 2 = 9, then 3 is the square root of 9. If b 2 = a, then b is the square root of a. If b.
OBJECTIVES: STUDENTS WILL BE ABLE TO… EVALUATE NTH ROOTS OF REAL NUMBERS USING RADICAL NOTATION AND RATIONAL EXPONENT NOTATION. 7.1: N TH ROOTS AND RATIONAL.
1 7.1 and 7.2 Roots and Radical Expressions and Multiplying and Dividing Radical Expressions.
Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.
§ 7.2 Radical Expressions and Functions. Tobey & Slater, Intermediate Algebra, 5e - Slide #2 Square Roots The square root of a number is a value that.
Section 1.2 Exponents & Radicals Objectives: To review exponent rules To review radicals To review rational exponents.
Section 7.2 So far, we have only worked with integer exponents. In this section, we extend exponents to rational numbers as a shorthand notation when using.
Rational Exponents When a base is raised to a rational exponent of the form 1/n we use the following definition: The denominator of the rational exponent.
Properties of Rational Exponents Lesson 7.2 Goal: Use properties of radicals and rational exponents.
+ 7.2 The Real nth Roots of a Number How many values in the domain of f are paired with the value in the range? That is, how many x values satisfy.
 The symbol is called a.  b is called the.  n is called the.  if n is, and if n is.  We can take an root of a negative number, but we cannot take.
Warm up 1. Change into Scientific Notation 3,670,900,000 Use 3 significant figures 2. Compute: (6 x 10 2 ) x (4 x ) 3. Compute: (2 x 10 7 ) / (8.
Exponents and Radicals Objective: To review rules and properties of exponents and radicals.
Roots and Radical Expressions
Warm-up Simplify each expression
Warm-up Write as a rational exponent. Answers:. Notes P3, Day 3: Cube Roots and Rational Exponents Definition of the Principal nth Root of a Real Number.
Radical Expressions and Functions Find the n th root of a number. 2.Approximate roots using a calculator. 3.Simplify radical expressions. 4.Evaluate.
Copyright © 2011 Pearson Education, Inc. Rational Exponents and Radicals Section P.3 Prerequisites.
Properties and Rules for Exponents Properties and Rules for Radicals
7-2 Properties of Rational Exponents (Day 1) Objective: Ca State Standard 7.0: Students add, subtract, multiply, divide, reduce, and evaluate rational.
Ch 8 - Rational & Radical Functions 8.8 – Solving Radical Equations and Inequalities.
7.1 Radicals and Radical Functions. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a.
Drill #67: Rationalize the denominators. (33.) Rational Exponents Definition: For any non-zero real b, and any integers m and n, with n > 1, Except when.
6-1 Radical Functions & Rational Exponents Unit Objectives: Simplify radical and rational exponent expressions Solve radical equations Solve rational exponent.
Chapter 7 – Powers, Roots, and Radicals 7.2 – Properties of Rational Exponents.
Rational (fraction) Exponents Please READ as well as take notes & complete the problems followed in these slides.
Entry Task– Simplify Expand then solve 3 5, 3 4, 3 3, 3 2 and 3 1 on a separate line in your notebook Now do 3 -1, 3 -2, 3 -3, 3 -4 and 3 -5 but leave.
Slide 7- 1 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Sections 8.1 and 8.2 Radical Expressions Rational Exponents.
Section 7.1 Rational Exponents and Radicals.
5.7 Rational Exponents Fraction Exponents.
6-1 Radical Functions & Rational Exponents
7.1 Warm-Up Evaluate the expression: √ √ √ Solve each equation.
Roots, Radicals, and Root Functions
7.1 nth roots and rational Exponents
Do Now: Simplify the expression.
Warm-up.
5.7 Rational Exponents Fraction Exponents.
1-6 Radicals (Day 1) and Rational Exponents (Day 2)
Roots of Real Numbers and Radical Expressions
Chapter 8 – Roots, Radicals and Rational Functions
7.5 Solving Radical Equations
Section 1.2 Exponents & Radicals
Evaluate nth Roots and Use Rational Exponents
7-5 Rational Exponents Fraction Exponents.
6.1 Nth Roots and Rational Exponents
Example 1: Finding Real Roots
5.7 Rational Exponents Fraction Exponents.
Roots of Real Numbers and Radical Expressions
7.6 Rational Exponents.
nth Roots and Rational Exponents
3.2 (Green) Apply Properties of Rational Exponents
7.1 Roots and Rational Exponents
Roots, Radicals, and Complex Numbers
3.2 Apply Properties of Rational Exponents
Do Now 1/17/19 Copy HW in your planner.
Rational Exponents and Radicals
Presentation transcript:

6-3: Rational Exponents Unit 6: Rational /Radical Equations

Recall: Exponent Rules Rational exponents behave exactly like the whole number exponents

Let’s look at some review problems

Definition of a rational exponent

Roots of nth roots CaseRootsExample Odd index1 real root Even index (positive radicand) 2 real roots Even index (negative radicand) No real roots radicand of 01 root of 0

Find all real roots

Simplifying nth roots Recall: and The same applies here: Ex.

Definition of a rational exponent A rational exponent is defined as: Where m and n are integers and n ≠ 0. Ex.

Write each expression in radical form and simplify. Write each expression using rational exponents. Solve.