Exponents, also referred to as Powers or Indices, are positive numbers placed above and to the right of a given quantity. Simply stated, exponents are the mathematical shorthand that instruct us to multiply the same number by itself for a specified number of times. Various mathematical rules exit regarding exponents, among them being the zero-exponent rule in which it is stated that raising anything to the zero power equals 1 (e.g. x o = 1), the product rule which states that to multiply two exponents with the same base one simply needs to maintain the base and sum the powers (e.g. x m . x k = x m+k) , and the negative exponent rule, which is the subject of this discussion.
A negative exponent is defined as the multiplicative inverse of the base raised to the positive opposite of the power. Stated otherwise, while a positive exponent tells us how many times to multiply a number by itself, a negative exponent is the inverse and tells us how many times to divide by the number. A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.
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For instance:
z -n
=
=
The negative exponent means that the base, the z , belongs on the other side of the fraction line. Therefore, we'll convert the expression into a fraction in the way that any expression can be converted into a fraction: by putting it over 1. After moving the base to the other side of the fraction line, there will be nothing left on top. But since anything can also be regarded as being multiplied by 1, we leave 1 on top.
Applying the negative exponent in solving a problem would play out as shown below.
Solve: m -3, where m = 2
m
-3 =
=
=
= 0.125
