Operating with Exponential Numbers
Exponents refer to positive or negative numbers that are placed above and to the right of a given quantity. The exponents serve to express the power to which the quantity is to be raised or lowered. For instance, in 5 4 ,4 is the exponent while 5 is known as the base. It shows that 5 is to be used as a factor four times. However, this post will focus mainly on negative exponents.
A negative exponent just indicates that the base is on the wrong side of the fraction line. Therefore, one has to basically flip the base to the other side. For example, 5 -4 is the same as 1/5 4 . In order to write x -3 using only positive exponents, one should remember that the negative exponents just means that the base, x, belongs to the other side of the fraction line. Therefore, the first thing should be to convert the expression, x -3 , into a fraction. Therefore, the final expression will look like this; 1/x 3 .
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Another expression could be x 2 /x -3 can also be expressed using positive exponents. One should not forget the main rule of thumb, that, a base with a negative exponent means that it is just on the wrong side of the fraction line. In this case, only one of the terms has a negative exponent. This means that only one of the terms will be moved to the opposite side of the fraction line. In this particular case, the term with a negative exponent is underneath. Therefore, the term x -3 will be move to the top of the fraction line as follows;
x 2 /x -3 = x 2 x 3 /1
=x 2+3 = x 5
From the illustration, it is clear that negative exponents indicate the times 1 can be divided by a given number. For instance, 5 -3 is the same as 1÷5÷5÷5 which is equal to 0.008.
