Unit 1 Day 4 Radical & Rational Exp. Practice

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Presentation transcript:

Unit 1 Day 4 Radical & Rational Exp. Practice Objectives: Simplify a rational exponent and radical expression by changing the base or factoring. Rewrite and evaluate a radical with rational exponents, and a number with a rational exponent in radical notation. Use properties of rational exponents to evaluate and simplify expressions. Standards: Apply and extend the properties of exponents to solve problems with rational exponents. Supplementary Reading: ???

Warmup Convert the following from radical to rational exponent notation or vice versa. Then Simplify 3 16𝑥 4 8𝑥 − 1 2

Applying What We Know Use the properties of exponents to rewrite the following See how the following are unable to be combined due to different bases…D-D-DROP THE BASE 2 2 =4 → 3 2 =9 → 4 5 9 3 4 5 9 3 = 1024 729 = ( 2 2 ) 5 ( 3 2 ) 3 = 2 10 3 6 2 10 3 6 5 1 3 ∗ 25 1 4 ∗𝑥 3∗5 1 5 −4∗ 25 2 5 +𝑥

Applying What We Know Expand the following 𝑥+2 2 𝑥 2 + 2 2 ≠ Does it Make sense that that would work with fractional exponents?... Look for another Method… 𝑥+2 2 𝑥+2 3 ≠ 𝑥 2 + 2 2 𝑥 3 + 2 3 𝑥 2 +4𝑥+4 1/2 3 𝑥 3 +4 𝑥 2 +2𝑥+8

Check For Understanding 2𝑥− 3 𝑥 3 𝑥 −5 3 𝑥 2 8 ( 4𝑥 2 −12𝑥+9) 3 ( 𝑥 3 −27)

Annoying Game!!! Get a sheet notebook paper out. Only calculators & Pencils. NO NOTES!!! Rules = answer the question on the board. Get called on. Claim your prize.

Vocab & Concepts Practice N nth root is simplified if the following 3 conditions are all true: 1.) 2.) 3.)

Vocab & Concepts Practice In 3 47 , the 3 is called the _________

Vocab & Concepts Practice In 3 47 , the 47 is called the _________

Vocab & Concepts Practice The process of moving removing the radical from the denominator is called ________________

Vocab & Concepts Practice What is the conjugate of 2- 𝑥 ?

Vocab & Concepts Practice What is the conjugate of 𝑥 +2?

Vocab & Concepts Practice What is the conjugate of 7−3 2𝑥 ?

Vocab & Concepts Practice What is the conjugate of 𝑥 − 3𝑥 ?

Practice Simplify Using Properties of Exponents

Practice Simplify Using Properties of Exponents

Practice Simplify Using Properties of Exponents

Practice Simplify Using Properties of Exponents

Practice Simplify Using Properties of Exponents

Practice Simplify Using Properties of Exponents

Practice Simplify Using Properties of Exponents

Practice Simplify Using Properties of Exponents

Closure Simplify the following 𝑥−2 ( 𝑥 2 −4𝑥+4)