English for Mathematics

1. EXPONENTS
What is an Exponent?
As you’ve been asked to write down three multiplied by three, remember you haven’t been
asked to calculate it. So pick up your pen and write it as three times three. Here we
multiply three by itself just once. Now, let say you’ve been asked to write down three
multiplied by three, multiplied by three. You write it down as three times three, times
three. In this example, we are multiplying three by itself twice. Three multiplied by itself,
multiplied by itself. Now, you’ve been asked to write down three multiplied by three,
multiplied by three, and so on seven times. So, may kind of bore. But you don’t have a
choice. So you write three times three, times three, times three, and so on seven times.
Yes, I know what you’re thinking, 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? What kind of operations that I’m talking
about here. The one in which a number is multiplied by itself many number of times. The
answer of that question is yes we do which raise us to the topic of exponents. Three
multiplied by three can be written as three with the two in the superscript. This is read as
three raised to two. How do we get the two? It depends on the number of threes you can
see. So we have two threes here. And hence, we write it as three raised to two. In the
second case, we can see three threes. Hence, it can be written as three raised to three.
How do we get three in the superscript? That’s because we have three threes. And in the
final example we have one, two, three, four, five, six, seven. Seven threes. So we write this
long strange of number seven threes as three raised to seven. If we have any number say
“a” multiplied by itself many times, we write “a” multiplied by “a”, multiplied by “a”,
multiplied by “a”, and so on. If there are “n” numbers of “a” in this product, then it can be
written as “a” raised to” n”. The number “a” is called the base, the number “n” is called
the exponent. In the three examples, we saw all of them have a based equal to three. It is
just the exponents that various. In the first case the exponent was two, in the second case
the exponent was three, and in the final example the exponent was seven.
Exponent Rules
When you multiply numbers with exponents that have the same base, you add the exponents
and keep the same base. Example, three squared times three cubed, equals three to the
two power plus three power, equals three 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, three to the sixth power divided by three squared, equals three to the six minus
two power, equals three to the fourth power. When you take an exponent of an exponent,
you multiply the exponents. Example, three squared cubed, equals three to the two times
three power, equals three to the sixth power. When you see a negative exponent, just put
one over that number with a positive exponent. Example, three to the negative two power,
equals one over three squared, equals one ninth. When you multiply, add the exponents.
When you divide, subtract the exponents. For an exponent of an exponent, you multiply.
For a negative exponent, take one over the positive. That’s exponents.