University:
University of South Alabama
Course:
PE 114 | Aerobics
Academic year:

2024
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433

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3
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customer-8570569

Name:____________________________________________ Date:_______________ Per:___ 5-2 Properties of Exponents and Radicals Radicals and Exponents are the same thing Warm-up: A. Simplify 3 B. Solve C. Simplify 5 10 6 4𝑥 = 400, 000 𝑥 12 18 64𝑥 𝑦 Today we are going to discuss properties of exponents, how they are similar to properties of radicals, and solving problems using each property. Properties: Product of Powers: Negative Exponents: Quotient of Powers: Zero as an Exponent: Power of Powers: Rational Exponents: Power of Product: Exponents of a Fraction: Example 1: Simplify the expression using the exponent properties: 5 6 1 −3 A. 81 • 81 B. ( 3 𝑥𝑦 1 ) 2 3 C. ( 𝑥2 9 2 ) 1 2 32 5 Example 2: Use the properties of radicals to rewrite radical expressions: 5 5 16 • 8 Step 1: Use the product property of radicals Step 2: Find the largest factor that is a fifth root of the radicand. Step 3: Reuse the product property of radicals and simplify. 1 Name:____________________________________________ Date:_______________ Per:___ You try: 3 9 A. 12 B. 27𝑥 14 49𝑥 • 3 6 8𝑥 Example 3: You can add and subtract radical expressions just like normal numbers. Radicals that can be added or subtracted are called ____________________________. These radicals will have the same index number, and the capability of having the same radicand, after simplification. Find the sum: 20 − 3 3 16 + 250 − 5 Step 1: Group radical terms together with common index numbers. Step 2: Simplify each radical. Step 4: Combine like terms. You Try: 3 3 A. 2, 000 + 2 − 128 B. 20 − 600 − 125 2 Name:____________________________________________ Date:_______________ Per:___ Warm-up: Simplify the following expressions: 3 6 A. 8𝑥 • 2𝑥 B. 3 9 8𝑥 18 125𝑦 Today we will be multiplying radicals and rationalizing radicals. Example 4: Multiplying Binomial Radical Expressions 3 3 A. 5(2 − 25) Step 1: Use distributive Property B. (2𝑥 − 3)(4𝑥 − 3) Step 1: Expand by using distributive property. Step 2: Multiply Radicands Step 2: Combine like terms. Step 3: Simplify the statement. You Try: A. (𝑥 − 10)(𝑥 + 10) B. 6(5 + 3) In You try A. this type of multiplication has a special name called _______________________. We can use this idea to aid us in simplifying division problems. Example 5: What is the conjugate of the expression? 1 2+ 5 You Try: A. 2 3− 𝑥 B. 5− 2 2− 3 3

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