Exponent Rules and Simplification

The video tutorial explains the quotient rule for exponents, which involves keeping the base the same and subtracting the exponents when dividing terms with the same base. Several examples are provided to illustrate this concept, including simplifying expressions with positive and negative exponents, as well as handling complex expressions with multiple bases.

What is the basic formula for the quotient rule of exponents?

• a^m + a^n = a^(m+n)

• a^m * a^n = a^(m+n)

• a^m - a^n = a^(m-n)

• a^m / a^n = a^(m-n)

In the quotient rule, what must be true about the base?

• The base must be zero.

• The base must be different.

• The base must be the same.

• The base must be negative.

What is the result of simplifying 3^9 / 3^2?

• 3^11

• 3^7

• 3^5

• 3^6

How many factors of 3 are left after simplifying 3^9 / 3^2?

• 5

• 6

• 7

• 8

What is the result of simplifying 14^23 / 14^6?

• 14^19

• 14^20

• 14^17

• 14^15

How many factors of 14 are left after simplifying 14^23 / 14^6?

• 19

• 15

• 17

• 18

What is the result of simplifying X^4 / X^3?

• X^2

• X^1

• X^3

• X^0

What is X^4 / X^3 simplified to?

• X^4

• X^3

• X

• X^2

In the expression 3^2 / 3^-7, what is the result after applying the quotient rule?

• 3^5

• 3^7

• 3^9

• 3^8

What is the result of simplifying y^5 / y^2?

• y^4

• y^5

• y^2

• y^3