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

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

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)

What is the cube root of -64?

• 4

• 8

• -8

• -4

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

• 7^2

• 7^4

• 7^3

• 7^1

What is the product rule for exponents?

• Multiply the bases

• Add the exponents

• Subtract the exponents

• Divide the bases

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

• 5^(1)

• 5^(3)

• 5^(4)

• 5^(2)

What is the fourth root of 81?

• 5

• 2

• 3

• 4