Negative Exponents and Their Applications

This lesson covers zero and negative exponents, explaining that any nonzero number raised to the zero power equals one, while a negative exponent indicates a reciprocal. The video provides examples and practice problems to reinforce these concepts, including real-world applications such as calculating water leakage over time.

What is the result of any nonzero number raised to the power of zero?

• Undefined

• One

• The number itself

• Zero

What is the value of 0 raised to the power of 0?

• Zero

• Infinity

• One

• Undefined

What does a negative exponent indicate?

• The base is negative

• The base is zero

• The reciprocal of the base raised to the positive exponent

• The exponent is zero

How would you express 4 to the power of -2?

• 1 over 4

• 4 squared

• 1 over 4 squared

• 4 to the power of 2

What is the result of 3 to the power of -4?

• 81

• 1 over 81

• 1 over 3

• 3

If you have a negative base raised to a negative power, what should you do first?

• Write the reciprocal of the base

• Add the exponents

• Multiply the base by itself

• Subtract the exponents

What is the result of simplifying 4 to the power of 5 divided by 4 to the power of 5?

• Four

• Undefined

• One

• Zero

How do you simplify an expression with a negative exponent in the denominator?

• Multiply by zero

• Leave it as is

• Subtract the exponent from the numerator

• Move it to the numerator and make the exponent positive

In the real-world problem, how many seconds are there in one hour?

• 120

• 1800

• 3600

• 60

What is the volume of water that leaks from the faucet in one hour, given the rate of 50 to the power of -2 liters per second?

• 0.36 liters

• 2.88 liters

• 0.72 liters

• 1.44 liters