Division Properties of Exponents Lesson 4.2 Division Properties of Exponents

Warm-Up Simplify. (3x4)2 (2a7b)(5a2b4) 2y3 ∙ (4y5)2 9x8 10a9b5 32y13

Division Properties of Exponents Lesson 4.2 Division Properties of Exponents Use properties of exponents to simplify expressions involving division.

Simplify the fractions by cancelling common factors. Good to Know! You have learned that when two powers with the same base are multiplied, the base remains the same and the exponents are added together. Examine the division problems below. When two powers with the same base are divided, the base remains the same and the exponents are subtracted. You can also simplify a power of a quotient or fraction by “distributing” the power to both the numerator and denominator. Simplify the fractions by cancelling common factors.

Division Properties of Exponents Quotient of Powers To divide two powers with the same base, subtract the exponents. Power of a Quotient To find the power of a quotient, find the power of the numerator and denominator.

Examples 1 & 2 Simplify the following. a. b.

Example 1 Simplify the following. a. Group powers that have the same base. Subtract exponents.

Example 2 Simplify the following. b. Distribute the power to each base. Multiply powers of powers and evaluate coefficients.

More Properties of Exponents Negative Exponents For any nonzero number a and integer n, the expression a −n is the reciprocal of an. Also, an is the reciprocal of a −n. Zero Exponents Any nonzero number, a, raised to the zero power is 1. Good to Know! An expression is in simplest form only if it has no negative or zero exponents. An exponent with its base can be moved to the opposite side of the fraction bar to change its sign.

Example 3 Simplify the following. a. Any term to the power of 0 equals 1.

Example 4 Simplify the following.

Example 4 Continued… Simplify the following. b. Write as separate factors. Use the rules for negative exponents. Multiply factors.

Example 5: CHALLENGE Simplify the following. c. Write as separate factors and group like bases. Simplify by subtracting exponents and dividing coefficients.

Example 5 Continued Simplify the following. c. Use rules for zero and negative exponents. Simplify.

4.2 Formative Assessment Simplify. 1. 2. 3. 4. 5. 6.