Exponentiation: Combining Exponential Terms

Professor Von Schmohawk introduces exponentiation, explaining it as repeated multiplication, similar to how multiplication is repeated addition. The lecture covers how to express numbers raised to powers, such as squared and cubed, and how to combine exponential expressions through multiplication and division. Key rules include adding exponents when multiplying expressions with the same base and subtracting exponents when dividing. The lecture concludes with a preview of future topics, including exponents of one, zero, and negative integers.

What does exponentiation simplify in mathematical operations?

• Repeated multiplication

• Repeated division

• Repeated subtraction

• Repeated addition

What is the base in an exponential expression?

• The number being raised

• The number being added

• The number being subtracted

• The number being multiplied

What is the term used when a number is raised to the power of 2?

• Doubled

• Cubed

• Halved

• Squared

What does 'cubed' mean in terms of exponentiation?

• Raised to the power of 2

• Raised to the power of 4

• Raised to the power of 5

• Raised to the power of 3

What happens when you multiply two exponential expressions with the same base?

• Add their exponents

• Multiply their exponents

• Divide their exponents

• Subtract their exponents

How do you calculate 4 squared times 4 cubed?

• 4 to the power of 6

• 4 to the power of 7

• 4 to the power of 5

• 4 to the power of 12

To multiply exponential expressions with the same base, you should:

• Subtract their bases

• Divide their exponents

• Add their exponents

• Multiply their bases

What is the result of 5 to the third power times 5 to the fourth power?

• 5 to the power of 5

• 5 to the power of 7

• 5 to the power of 12

• 5 to the power of 8

What is the result of dividing 5 to the seventh power by 5 to the fourth power?

• 5 to the power of 3

• 5 to the power of 7

• 5 to the power of 11

• 5 to the power of 4

What operation do you perform on the exponents when dividing two exponential expressions with the same base?

• Addition

• Multiplication

• Subtraction

• Division