Understanding negative exponents

Learning Objectives Define what a negative exponent represents. Rewrite expressions with negative exponents as equivalent expressions with positive exponents. Evaluate numerical expressions containing negative exponents. Understand the relationship between a number raised to a positive exponent and the same number raised to a negative exponent. Simplify expressions involving negative exponents by converting them to fractional form. Apply the concept of negative exponents to represent very small quantities. Ever wondered how scientists talk about things smaller than a tiny speck of dust? 🔬 Negative exponents help us describe incredibly small numbers in a neat way! In this lesson, you'll discover what negative exponents mean and how they're used to represent fracti...

TermDefinitionExample ExponentThe small number written above and to the right of a base number, indicating how many times the base is multiplied by itself.In 2³, 3 is the exponent. BaseThe number that is being multiplied by itself, as indicated by the exponent.In 2³, 2 is the base. Positive ExponentAn exponent that is a positive integer, indicating repeated multiplication of the base.5² = 5 × 5 = 25 Negative ExponentAn exponent that is a negative integer, indicating the reciprocal of the base raised to the positive version of that exponent.2⁻³ = 1/2³ ReciprocalThe number you multiply by another number to get 1. For a number 'a', its reciprocal is 1/a. For a fraction a/b, its reciprocal is b/a.The reciprocal of 5 is 1/5. The reciprocal of 2/3 is 3/2. FractionA number that represe...

Definition of Negative Exponent a^{-n} = \frac{1}{a^n} Any non-zero base 'a' raised to a negative exponent '-n' is equal to the reciprocal of the base raised to the positive exponent 'n'. This rule is used to convert expressions with negative exponents into expressions with positive exponents, which are easier to evaluate. Negative Exponent in the Denominator \frac{1}{a^{-n}} = a^n If a base 'a' raised to a negative exponent '-n' is in the denominator of a fraction, it can be moved to the numerator by changing the exponent to positive 'n'. This is essentially applying the reciprocal rule twice. Negative Exponent with a Fractional Base \left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n When a fraction...