English for Mathematics

1. What is exponent ?
As you’ve been asked to write down two multiplied by two,remember you haven’t been asked
to calculate it. So pick up your pen and write it as two times two. Here we multiplytwo by it
self just once. Now, let say you’ve been asked to write down two multiplied by two,
multiplied by two. You write it down as two times two, times two. In this example, we are
multiplying two by it self twice. Two multiplied by it self, multiplied by it self. Now, you’ve
beenasked to write down two multiplied by two, multiplied by two, and so on six times. So
may kind of bore. But you have don’t choice. So you write two times two, times two, times
two, and so on six times. Yes I know what you are thinking, the more number of time you
multiply a number by it self, the more tedius it gets for you to write it down. So that raises us
the question. Is there an easier way to denote this kind of operation what kind of operations
that I am taking about here. The one in which a number is multiplied by it self many number
of times. The answer of that question is yes we do which raise us to the topic of exponents,
two multiplied by two can be written as two with the two in the superscript. this is read as
two raised to two. How do we get the two ? it depends on the number of twos you can see. So
we have two twos here. And hence, we write it as two raised to two. In the second case, we
can see three twos. Hence, it can be written as two raised to three. How do we get three in
the superscript ? that because we have two threes and in the final example we have six twos.
So we write this long strang of number six two as two raised to six. If we have any number say
“b” multiplied by “a” and so on. If there are “m” numbers of “b” in this product, then it can
be written as “b” raised to “m”. the number “b” is called the base, the number “m” is called
the exponent. In the three examples, we saw all of them have a based equals to two. It is just
the exponents that various. In the first case the exponent was two, in the second case
exponent was three and in the final example the exponent was six.
Exponents Rules
When you multiply numbers with exponents that have the same base, you add the exponents
and keep the same base. Example, four cubed times four squared, equals four to the three
power plus two power, equals four to the fifth power. When you divide numbers with
exponents that have the same base, you subtract the exponents and keep the same base.
Example, four to the ninth power divided by four squared. Equals four to the nine minus
two power equals four to the seventh power. When you take when exponent of an exponent,
you multiply the exponents. Example, four cubed squared equals four to the three times two
power, equals four to the sixth power. When you see a negative exponent, just put one over
number with a positive exponent. Example, four to the negative three power equals one over
four cubed, equals one over sixty four. When you multiply, add the exponents. When you
divide, subtract the exponents. For an exponent of an exponent, you multiply. For a negative
exponenet, take one over the positive. That’s exponents.