English for Mathematics

1. EXPONENT
What is Exponent?
As you’ve been asked to wite down five multiplied by five, remember you haven’t
been asked to calculate it. So pick up your pen and write it as five times times. Here we
multiply five by itself just once.
Now, let say you’ve been asked to write down five multiplied by five, multiplied by
five. You write it down as five times five, times fives. In this examples, we are multiplying
five by itself twice. Five multiplied by itself, multiplied by itself.
Now, you’ve been asked to write down five multiplied by five, multiplied by five, and
so on six times.
So, may kind of bore. But you don’t have a choic e. So, you write five times five,
times five, times five, and so on six times. The more number of time you multiply a number
by itself, the more tedious it gets for you to write it down. So that raises us to the question. Is
there an easier way to denote this kind of operations? The one in which a number is
multiplied by itself many number of times. The answer of that question raise us to the topic of
exponents.
Five multiplied by five can be written as five with the two in the superscript. This is
read as five raised to two.
How do we get the two? It depends one the number of fives you can see. So we have
two fives here. And hence, we write it as five raised to two.
In the second case, we can see four fives. It can be written as five raised to four. We
have four in the superscript because we have four fives.

2. And in the final example, we have one, to, three, four, five, six. Six fives. So we write
this long strange of number six fives as five raised to six.
If we have any number say ‘b’ multiplied by itself many times, we write b multiplied
by b, multiplied by b, multiplied by b, and so on. If there are ‘n’ numbers of ‘b’ in this
product, then it can be written as b raised to n. The number b is called the base, the number n
is called the exponent.
In the three examples, we saw all of them have a based is equal to five. It is just the
exponents that various. In the first case the exponent was two, in the second case the
exponent was four, and in the final example the exponent was six.
Exponent Rules
When you multiply numbers with exponents that have the same base, you add the
exponents and keep the same base. For example is, six squared times six to the fourth power
equals six to the two plus four power equals six to the sixth power.
When you divide numbers with exponents that have the same base, you subtract the
exponents and keep the same base. For example is, six to the eighth power divided by six
cubed equals six to the eight minus three power equals six to the fifth power.
When you take an exponent of an exponent, you multiply the exponents. For example
is, four squared cubed is equal to four to the two times three power equals four to the sixth
power.

3. When you see a negative exponent, just put one over that number with a positive
exponent. Example, five to the negative two power equals one over five squared equals one
over twenty five.
When you multiply, add the exponents. When you divide, subtract the exponents. For
an exponent of an exponent, multiply the exponents. For a negative exponent, take one over
that number with the positive exponent. That’s exponent.