Exponent Rules and Simplification

This lesson covers multiplying rational exponents, focusing on like bases and variables. It explains how to add exponents when multiplying like bases and how to handle different types of exponents, including those with common denominators. The video also explores radicals and cube roots, demonstrating how to simplify them. Finally, it discusses raising bases to rational exponents and the rules for multiplying exponents.

What is the result of multiplying 2^(2/3) by 2^(4/3)?

• 2^(8/3)

• 4

• 8

• 2^(6/3)

When multiplying x^(1/8) by x^(5/8) and x^(1/8), what is the simplified exponent?

• 7/8

• 1

• 3/8

• 5/8

How do you simplify the expression 2^(3/4) * 2^(1/3)?

• 2^(4/3)

• 2^(1/12)

• 2^(13/12)

• 2^(7/12)

What is the cube root of 7 times the cube root of 2 simplified to?

• Cube root of 9

• Cube root of 14

• Cube root of 49

• Cube root of 4

What is the simplified form of the cube root of 9 times the cube root of 9?

• 9 cube root of 9

• Cube root of 81

• Cube root of 18

• 3 cube root of 3

How do you simplify y^(2/3) raised to the power of 5/2?

• y^(7/3)

• y^(1/3)

• y^(5/3)

• y^(10/6)

What is the result of raising x^(1/2) * x^(3/4) to the power of 2?

• x^(5/2)

• x^(3/2)

• x^(1)

• x^(7/4)

When multiplying like bases, what operation is performed on the exponents?

• Add the exponents

• Subtract the exponents

• Divide the exponents

• Multiply the exponents

What is the simplified form of y^(3/5) raised to the power of 1/6?

• y^(1/2)

• y^(1/5)

• y^(1/30)

• y^(1/10)

How do you simplify x^(1/2) * x^(3/4) when raised to the second power?

• x^(3/2)

• x^(1)

• x^(7/4)

• x^(5/2)