Exponent, What is exponent
If you multiply a.a it's easy to write down, but when you have to multiply a.a.a.a.a.a... fourty five times for example, there is much more to write down, so we use a shorter fuction, called exponent(power). Remember exponent can be used only when multiplying the same values. This is how it looks the write down of 45 times a.a.a.a.a.a... with exponent - a45 . The upper index indicates the number of multipliers in the function, and it's called exponent, and a is called a base. The index of an exponent refers only for the value that is directly attached to or a group of values in parentheses.
An exponent can accept values both positive and negative. When it's negative the following rule applies - x-a = 1/xa, but there is a restriction of divideing by null, so x must be different from null.
Exponents can accept values from the multitude of the real numbers. They can be both rational or irational. When the exponent is fractional, for example 3/4, the divider, in this case 4, means to take the 4-th root of x3. For more details read materials for radicals.
Laws of Exponents:
Those are the basic equations, which you need to remember.
If you have an.am that equals a.a.a.a.a...(n times).a.a.a.a.a.....(m times) which equals a.a.a.a.a....(n + m times) or am + n
this case is the oposite of the previous (if a is different from null)
If you have (an)m that equals (a.a.a.a.a...(n times)).(a.a.a.a.a...(n times)).(a.a.a.a.a...(n times)) ...... (m times) in this case the number of multipliers is n times m and then this (an)m equals to am.n.
If you have (a.b)n this equals to (a.b).(a.b).(a.b)....(n times) which equals to (a.a.a.a.a...(n times)) . (b.b.b.b.b....(n times) or an.bn.
This case is the oposite of the previous (b is different from null).
Exponent Function Monotony
If 0 < x < y then:
- if r > 0 => xr < yr
- if r < 0 => xr > yr
If x < y and they are rational
-if 0 ≤ a < 1 => ax > ay
-if a > 1 => ax < ay
More about exponents in the maths forum