Simplifying Quotients with Negative Exponents

This video tutorial explains how to simplify quotients with negative exponents when the bases are not the same. It emphasizes that the quotient rule of exponents cannot be applied in such cases. Instead, the video demonstrates how to make exponents positive by moving terms across the fraction bar, changing the sign of the exponents. Several examples are provided to illustrate the process, showing step-by-step how to simplify expressions by adjusting the position of terms and evaluating the results.

Why can't the quotient rule of exponents be applied when the bases are different?

• Because the exponents are positive.

• Because the bases are positive.

• Because the bases must be the same to apply the rule.

• Because the exponents are negative.

What happens to the sign of an exponent when it is moved across the fraction bar?

• It becomes zero.

• It remains the same.

• It doubles.

• It changes to the opposite sign.

Which rule is applied to change the sign of an exponent when moving it across the fraction bar?

• Fraction rule

• Addition rule

• Exponent rule

• Multiplication rule

What is the simplified form of moving 2^-3 to the numerator?

• 2^3

• 2^-3

• 3^2

• 3^-2

In the first example, what is the simplified form of 2^-3 / 3^-2?

• 7/6

• 6/7

• 9/8

• 8/9

What is the result of simplifying 5^2 / 2^-3?

• 200

• 150

• 100

• 50

In the second example, what is the value of 5^2?

• 20

• 10

• 25

• 15

In the final example, what is the simplified form of 3^-1 / 4^2?

• 1/48

• 1/16

• 1/12

• 1/64

What is the simplified result of 3^3 / 1^-2?

• 108

• 27

• 54

• 81

What is the main goal when simplifying quotients with negative exponents?

• To make the bases equal.

• To make the exponents positive.

• To make the exponents negative.

• To make the bases negative.