Evaluate negative exponents

Learning Objectives Define what a negative exponent represents. Convert expressions with negative exponents into equivalent expressions with positive exponents. Evaluate numerical expressions containing negative integer exponents. Simplify expressions involving negative exponents to their simplest fractional or integer form. Identify and correct common errors when evaluating negative exponents. Apply the rule for negative exponents to solve basic mathematical problems. Have you ever seen a number raised to a 'negative power' and wondered what it means? 🤔 It's like asking a number to do the opposite of multiplying! In this lesson, you'll uncover the secret behind negative exponents and learn how to transform them into something you can easily calculate....

TermDefinitionExample BaseThe number that is being multiplied by itself in an exponential expression.In $2^{-3}$, the base is 2. ExponentThe small number written above and to the right of the base, indicating how many times the base is multiplied by itself (or its reciprocal for negative exponents).In $2^{-3}$, the exponent is -3. Negative ExponentAn exponent that is a negative number. It indicates that the base should be taken as a reciprocal before being raised to the positive version of the exponent.$5^{-2}$ means the reciprocal of $5^2$. ReciprocalFor any non-zero number, its reciprocal is 1 divided by that number. If the number is a fraction, you 'flip' it (swap numerator and denominator).The reciprocal of 3 is $\frac{1}{3}$. The reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$...

Rule of Negative Exponents $a^{-n} = \frac{1}{a^n}$ 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 allows us to convert negative exponents into positive ones, making them easier to evaluate. Negative Exponent in the Denominator $\frac{1}{a^{-n}} = a^n$ If a base 'a' raised to a negative exponent '-n' appears 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.