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
=
