Negative Exponent Rules
Negative exponents use all the basic exponent rules and other than that there are two basic negative exponents rules which are used to simplify the negative exponents which are,
Rule 1: We can simplify the negative exponent by first taking the reciprocal of the base and then solving for the positive power of the base, i.e. if the negative exponent a-n is to be solved we first take the reciprocal of the base (1/a) and then solve it for its nth power. This can be easily understood as,
a(-n) = 1/a × 1/a × … n times = 1/an
Rule 2: In this rule, we tend to solve for a negative exponent in the denominator if there is a negative exponent in the denominator then it is transported to the numerator and its negative sign is removed. We can understand this by the formula,
1/a(-n) = a × a × … .n times = an
The negative exponent’s rule can be easily understood with the example discussed in the image below,
These rules can be easily understood by the example discussed below,
Example: Simplify 3-3 × 1/(4-2)
Solution:
Using the above rule for solving negative exponents,
a-n = 1/an and 1/a(-n) = an
3-3 = 1/33
= 1/27
1/(4-2) = 42
= 16
Now, 3-3 × 1/(4-2)
= 1/27 × 16
= 16/27
Negative Exponents
Negative Exponents are the exponents with negative values. In other words, negative exponents are the reciprocal of the exponent with similar positive values, i.e. a-n (a negative exponent) can be understood as the reciprocal exponent as 1/an.
We can understand the concept of negative exponents by the following example, find the value of (1/2)-2 we can write this exponent as, (2/1)2 this can be further simplified as, 4/1 or 4.
Let us learn more about what are negative exponents, their examples with solutions, practice problems, and others in detail in this article.
Table of Content
- What are Negative Exponents?
- Negative Exponents Definition
- Representation of Negative Exponents
- Negative Exponent Formula
- Expressions with Negative Exponents
- Negative Exponent Rules
- Negative Exponents are Fractions
- Negative Fraction Exponents
- Multiplying Negative Exponents
- How to Solve Negative Exponents?
- Negative Exponents Examples with Solutions
- Negative Exponents Worksheet
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