Question

UNIT 5
Polynomials and Properties of Exponents
LESSON 5
Exponents and Division

Answer 1

x^9/x^2

Answer 2

One property of exponents that is important to understand when dividing with exponents is the quotient rule. This rule states that when dividing two terms with the same base, you can subtract the exponents.

For example, if you are dividing x^3 by x^2, you can use the quotient rule to simplify as follows:

x^3 / x^2 = x^(3-2) = x^1 = x

Another important concept to understand is how negative exponents work. Remember that a negative exponent means you are taking the reciprocal of the base raised to the positive exponent.

For example, if you have x^-2, this equals 1 over x^2. And if you have (1/x)^-3, this equals x^3.

When dividing with negative exponents, it can be helpful to first rewrite the expression so that all exponents are positive. Then, you can apply the quotient rule.

For example, if you have x^-2 / y^-3, you can rewrite this as (y^3 / x^2) and then use the quotient rule as follows:

x^-2 / y^-3 = (y^3 / x^2) = y^(3-(-2)) / x^(2-(-3)) = y^5 / x^5

Overall, when dividing with exponents, it's important to keep track of the base and the exponent of each term and use the quotient rule and/or understanding of negative exponents as necessary.

Answer 3

Using the quotient rule, we can simplify x^9/x^2 as follows:

x^9 / x^2 = x^(9-2) = x^7

Therefore, x^9/x^2 simplifies to x^7.