Negative Exponents

This lesson teaches how to simplify expressions with negative exponents. It begins by explaining the concept of negative exponents using a chart of powers of 3, showing how values decrease as exponents become negative. The lesson identifies patterns and explains that a number raised to a negative exponent is the reciprocal of the number raised to the corresponding positive exponent. A formal definition is provided, stating that a to the power of negative n equals 1 over a to the power of n. The lesson concludes with an example of simplifying 4 to the power of negative 2, resulting in 1/16.

What happens to the value of a power of 3 as the exponent decreases?

• It remains the same.

• It increases.

• It decreases.

• It becomes negative.

How is 3 to the power of negative 3 related to 3 to the power of 3?

• They are equal.

• They are reciprocals.

• One is double the other.

• One is half the other.

What is the result of moving a negative exponent from the numerator to the denominator?

• It becomes zero.

• It remains negative.

• It becomes positive.

• It becomes a fraction.

According to the definition, what does a to the power of negative n equal?

• 1 over a to the power of n

• a to the power of n

• 1 over a to the power of negative n

• a to the power of negative n

What is the simplified form of 4 to the power of negative 2?

• 16

• 1/4

• 1/16

• 4