Properties of Exponents and Simplification

The video tutorial explains the properties of exponents, focusing on the product and power properties. It provides examples to illustrate how to multiply exponents with the same base and how to handle powers raised to powers. The tutorial also covers evaluating numerical bases and fractional exponents, emphasizing verification through expansion.

What does the product property of exponents state?

• Subtract the exponents and divide the bases.

• Multiply the bases and add the exponents.

• Add the bases and multiply the exponents.

• Keep the base the same and add the exponents.

In the expression Y^3 * Y^4, what is the resulting exponent of Y?

• 4

• 3

• 7

• 12

When multiplying 2^2 and 2^3, what is the base of the result?

• 6

• 4

• 5

• 2

What is the value of 2^5?

• 16

• 8

• 32

• 64

How do you simplify (2^3)^2 using the power property?

• 2^8

• 2^5

• 2^6

• 2^9

What is the result of 3^3?

• 27

• 9

• 81

• 18

In the expression (3Z^3)^3, what is the exponent of Z?

• 6

• 9

• 3

• 12

How do you simplify (X^4/6)^2?

• X^8/36

• X^8/12

• X^2/12

• X^4/36

What is the value of 6^2?

• 12

• 18

• 36

• 24

What happens to the exponents when a fraction is raised to a power?

• Only the numerator is raised to the power.

• Only the denominator is raised to the power.

• Both numerator and denominator are raised to the power.

• The fraction remains unchanged.