Exponent is the number that is made with two numbers. One is known as base which is followed by another number generally written in the superscript. The second number in the exponent is known as power. As the name suggests ‘negative exponent’ is the number whose power or exponent happens to be negative. A negative exponent is generally of the following form 3^-2.
In mathematics however this is not the proper form of writing a number with power. Therefore, the expression of negative exponent has to be in the appropriate form. The proper form of negative exponent is as follows
The easiest way to deal with negative exponent is to keep in mind that negative is the reverse of positive and the reverse of multiplication is division. Therefore, a number having negative exponent has to be moved to denominator in the fractional form. After moving to the denominator, the exponent turns out to positive. The reverse is also true. If there is a negative exponent in the denominator of a fraction, then the exponential term is moved to the numerator along with a change in sign.
For example, 3^-2 becomes 1/3^2
In order to complete calculation with negative exponents one needs to understand the basic rules related to use of exponents. The basic exponent rules related to four main operations such as addition, subtraction, multiplication and division.
The simplest operations with exponential number are addition and subtraction. For adding negative exponent, a number raise to the power can be added to another number that is raised to a power (with either different exponent or a different base) after calculating exact number from the exponential term. Once the exact numbers from the exponential expression are obtained they can be added directly.
Similar rule is applicable for subtraction of negative exponents. For numerical negative exponential term, the exponential terms are first converted into simple numbers and then the operation is performed.
If base and powers of negative exponent terms matches with each other, addition and subtraction can be performed in the similar way like matching the symbols in simple algebra.
Multiplication with exponents is possible only when two exponents have the same base. The general rule for multiplying negative exponents is to add power of the number. A negative exponent implies division of base raised to the power of exponent into 1. Therefore, X5 * X-3 actually means X5 * 1/X3.
In other words, when a number is multiplied by negative exponent, one still add the exponent. However, since is negative exponent, this is more like subtracting the number. The general rule therefore is,
For division of exponential number, the general rule is subtract the powers. When a number is divided by a negative exponent number, it is similar to multiplying the same exponent only with positive power.
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