Splash Screen Unit 6 Exponents and Radicals

Splash Screen Essential Question: How do you evaluate expressions involving rational exponents?

Lesson Menu 5 minute check on Unit 5. Do the first 5 problems!

Over Lesson 7–2 5-Minute Check 1 A.49 B. C. D.

Over Lesson 7–2 5-Minute Check 2 A. B. 2n 4 C. D.

Over Lesson 7–2 5-Minute Check 3 A. B. C. D.

Over Lesson 7–2 5-Minute Check 4 A. B. C. D.

Over Lesson 7–2 5-Minute Check 6 A.B. C.D.

Then/Now You used the laws of exponents to find products and quotients of monomials. Evaluate and rewrite expressions involving rational exponents. Solve equations involving expressions with rational exponents. EQ: How do evaluate expressions involving rational exponents?

Vocabulary rational exponent radical cube root nth root exponential equation

What is a rational number? A rational number is any number that can be expressed as the quotient or fraction of two integers, with the denominator not equal to zero.

What is a RADICAL? If n is a positive integer that is greater than 1 and a is a real number then, where n is called the index, a is called the radicand, and the symbol √ is called the radical.

Square Root - easy definition A number that when multiplied by itself equals a given number. Root A number that, when multiplied by itself some number of times, equals a given number.

Perfect Squares 1 2 = = = = = = = = = = = = 144 Perfect Cubes 1 3 = = = = = = = = = = = 1, = 1,728

Concept Square Root

Example 1A Radical and Exponential Forms Answer: 9 Write each expression in radical form, or write each radical in exponential form. = 9Simplify.

Example 1B Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form. Answer:

Example 1C Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form. Answer:

Example 1D Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form. Answer: 9

Example 1CYP A.16 B.8 C.4 D.2

Example 1CYP Write each expression in radical form.

Example 1CYP Write each radical in exponential form.

End of the Lesson Assignment: Do Worksheet #1 to #9 Assignment: Do Worksheet #1 to #9 EQ: How do you evaluate expressions involving rational exponents?

Concept

Example 2A nth Roots A. Answer: 4

Example 2B nth Roots B. Answer: 5

Example 2A A.343 B.81 C.49 D.7

Example 2A Simplify.

Concept

Cube Root nth Root

Example 3 Evaluate b Expressions Answer: 11 A. = 11Simplify.

Example 3 Evaluate b Expressions Answer: 7 = 7Simplify. B.

Example 3 A.4 B.8 C.16 D.32

Example 3 Simplify.

End of the Lesson Assignment: Do Worksheet #10 to #18 Assignment: Do Worksheet #10 to #18 EQ: How do you evaluate expressions involving rational exponents?

Concept

Example 4A Evaluate b Expressions Answer: 4 = (2) = 32 = 4Simplify.

Example 4B Evaluate b Expressions Answer: 59,049 = (9) = 81 = 59,049Simplify.

Example 4 A.216 B.36 C.18 D.6

Example 4 Simplify.

End of the Lesson Assignment: Do Worksheet #19 to #21 Assignment: Do Worksheet #19 to #21 EQ: How do you evaluate expressions involving rational exponents?

Concept

Example 5A Solve Exponential Equations A. Solve 9 x = x = 729 Original equation 9 x = 9 3 Rewrite 729 as 9 3. x= 3 Power Property of equality

Example 5B Solve Exponential Equations B. Solve 16 2x – 1 = x – 1 = 8 Original equation (2 4 ) 2x – 1 = 2 3 Rewrite 16 as 2 4 and 8 as x – 4 = 2 3 Power of a Power, Distributive Property 8x – 4= 3 Power Property of Equality 8x = 7 Add 4 to each side. Divide each side by 8.

Example 5A Solve 9 3 x + 1 = A. B. C. D.2

Example 5A Solve 6 x = 216.

Example 5A Solve each equation. Solve 25 x - 1 = 5.

End of the Lesson Assignment: Complete the Worksheet EQ: How do you evaluate expressions involving rational exponents?