Exponent Rules and Properties

Professor Dave introduces exponents, explaining their role in arithmetic as repeated multiplication. He illustrates exponential growth with a chess legend, showing how quickly numbers can grow. The video covers examples of exponents, including negative exponents, and explains the rules for manipulating terms with exponents, such as addition, subtraction, and multiplication of exponents.

What does the exponent in a number indicate?

• The number of times the base is subtracted

• The number of times the base is added

• The number of times the base is multiplied

• The number of times the base is divided

What is the correct way to express 5 to the fourth power using the hat symbol?

• 5^3

• 5^4

• 5^6

• 5^5

In the chessboard legend, how many grains of rice are on the final square?

• Over a trillion

• Over a quintillion

• Over a billion

• Over a million

What is the result of 3 raised to the fourth power?

• 64

• 81

• 27

• 243

How do you calculate a negative exponent, such as 2 to the power of -2?

• Add the base to itself

• Subtract the base from itself

• Divide 1 by the base raised to the positive exponent

• Multiply the base by itself

What is the result of multiplying X to the power of A by X to the power of B?

• X to the power of A plus B

• X to the power of A minus B

• X to the power of A times B

• X to the power of A divided by B

What happens when you divide X to the power of A by X to the power of B?

• X to the power of A divided by B

• X to the power of A minus B

• X to the power of A times B

• X to the power of A plus B

What is the result of raising X to the power of A to the power of B?

• X to the power of A plus B

• X to the power of A times B

• X to the power of A divided by B

• X to the power of A minus B

Why is anything raised to the zero power equal to one?

• Because it cancels out to zero

• Because all terms cancel out leaving one

• Because it represents no multiplication

• Because it is undefined

What mistake should be avoided when dealing with terms like X to the A plus X to the B?

• Assuming they can be combined

• Assuming they are zero

• Assuming they are negative

• Assuming they are equal