Zero, negative, and fractional exponents
- 2. Learning Objectives • Simplify expressions with negative exponents. • Simplify expressions with zero exponents. • Simplify expression with fractional exponents. • Evaluate exponential expressions.
- 3. The product and quotient rules for exponents lead to many interesting concepts. For example, so far we’ve mostly just considered positive, whole numbers as exponents, but you might be wondering what happens when the exponent isn’t a positive whole number. What does it mean to raise something to the power of zero, or -1, or 12 ? In this lesson, we’ll find out. Introduction
- 4. we saw that it applies even when the exponent in the denominator is bigger than the one in the numerator. Cancelling out the factors in the numerator and denominator leaves the leftover factors in the denominator, and subtracting the exponents leaves a negative number. So negative exponents simply represent fractions with exponents in the denominator. This can be summarized in a rule: QUOTIENT RULE FOR EXPONENTS
- 5. Negative Power Rule for Exponents: 1. using the power rule 2. using the negative power rule separately on each variable 3. using the power rule for quotients 4. using the negative power rule on each variable separately 5. simplifying the division of fractions 6. using the power rule for quotients in reverse.
- 6. Write the following expressions without fractions. Negative Power Rule for Fractions: EXAMPLE 1. 1 𝑥 = 𝑥−1 2. 2 𝑥2 = 2𝑥−2 3. 𝑥² 𝑦³ = 𝑥2 𝑦−3 4. 3 𝑥𝑦 = 3𝑥−1 𝑦−1 5. 3𝑎² 3𝑎²𝑏³ =𝑏−3
- 7. Simplify the following expressions and write them without fractions. Practice 1. 𝟒𝒂 𝟐 𝒃 𝟑 𝟐𝒂 𝟓 𝒃 = 2. ( 𝟐𝒙 𝒚 𝟐)³ . 𝒙 𝟐 𝒚 𝟒 =
- 8. SEATWORK Write the following expressions without negative exponents.