Power and Exponent Rules

The video tutorial explains the power of a power property in mathematics, which involves raising a number or variable to a power and then raising the result to another power. The tutorial demonstrates two methods to evaluate such expressions: directly calculating the inner power and then the outer power, or using the product of powers property to simplify the expression. The video also covers examples with both numbers and variables, illustrating how to apply the power of a power property. Finally, practice problems are provided to reinforce the concept.

What is the result of raising 2 cubed to the second power?

• 128

• 16

• 32

• 64

Which method involves evaluating the expression inside the parentheses first?

• Outside-in method

• Inside-out method

• Quotient of powers method

• Product of powers method

How many times do you multiply 2 cubed when raising it to the 5th power?

• 8 times

• 5 times

• 10 times

• 3 times

What is the result of x squared raised to the fourth power?

• x to the 4th

• x to the 6th

• x to the 8th

• x to the 10th

What is the general rule for the power of a power property?

• a^(n*m)

• a^(n+m)

• a^(n/m)

• a^(n-m)

What is the simplified form of 2 squared raised to the fifth power?

• 2 to the 10th

• 2 to the 5th

• 2 to the 15th

• 2 to the 20th

What is the value of 2 to the 15th power?

• 4096

• 8192

• 16384

• 32768

How do you simplify x cubed raised to the fourth power?

• x to the 10th

• x to the 7th

• x to the 12th

• x to the 15th

What is the result of x squared raised to the fifth power in the denominator?

• x to the 8th

• x to the 12th

• x to the 10th

• x to the 5th

Using the quotient of powers property, what is x to the 12th divided by x to the 10th?

• x to the 5th

• x to the 4th

• x cubed

• x squared