Simplifying Radical Expressions and Rational Exponents

This video tutorial covers radical expressions and rational exponents, starting with basic vocabulary and types of radicals. It explains how to determine the number of real roots based on the index and radicand. The tutorial then transitions to rational exponents, demonstrating how to convert between radicals and rational expressions. It reviews key exponent rules, including the product, power, and quotient rules, and applies these rules to simplify expressions. The video concludes with practical examples to reinforce the concepts discussed.

What is the term for the number under the radical sign?

• Index

• Exponent

• Root

• Radicand

Tags

CCSS.8.NS.A.1

How many real roots does the fourth root of 81 have?

• Three

• One

• None

• Two

What is the cube root of -8?

• -2

• 2

• -4

• 4

Tags

CCSS.8.EE.A.2

What is the prime factorization of 224?

• 2^6 * 7

• 2^3 * 7

• 2^4 * 7

• 2^5 * 7

How can you rewrite 4^(3/2) as a radical expression?

• 4^(1/2)^3

• √(4)^3

• 3√(4^2)

• √(4^3)

Tags

CCSS.HSN.RN.A.2

What is the cube root of -64?

• 4

• 8

• -8

• -4

Tags

CCSS.8.EE.A.2

How would you simplify the expression 7^(4/2)?

• 7^2

• 7^4

• 7^3

• 7^1

Tags

CCSS.HSN.RN.A.2

What is the product rule for exponents?

• Multiply the bases

• Add the exponents

• Subtract the exponents

• Divide the bases

Tags

CCSS.8.EE.A.1

What is the simplified form of 5^(2/3) * 5^(1/3)?

• 5^(1)

• 5^(3)

• 5^(4)

• 5^(2)

Tags

CCSS.HSN.RN.A.2

What is the fourth root of 81?

• 5

• 2

• 3

• 4