### Video Transcript

Calculate 8.2 multiplied by 10 to
the fourth power divided by 4.1 multiplied by 10 to the second power, giving your
answer in scientific notation.

In this question, we’ve been given
two values to divide, each in scientific notation, or standard form. This means that these numbers have
been written in the form 𝑎 multiplied by 10 to the 𝑛th power, where the modulus of
𝑎 is greater than or equal to one and less than 10 and 𝑛 is an integer.

Let’s begin by rewriting the
expression in this way: 8.2 multiplied by 10 to the fourth power over 4.1 multiplied
by 10 to the second power. Writing it in this way helps us to
then rewrite the division as a multiplication of two fractions. This is 8.2 over 4.1 multiplied by
10 to the fourth power over 10 to the second power. Now, let’s simplify each of these
two fractions.

Firstly, we can evaluate 8.2 over
4.1. That gives us two. Then, we can evaluate 10 to the
fourth power over 10 to the second power. To do this, let’s recall the
exponent quotient rule. That is, 𝑥 to the 𝑚 power over 𝑥
to the 𝑛 power equals 𝑥 to the 𝑚 minus 𝑛 power. Therefore, 10 to the fourth power
over 10 to the second power is 10 to the four minus two power. And because four minus two is two,
this is 10 to the second power or 10 squared.

So, our answer is two multiplied by
10 to the second power. Remember that we were asked to give
our answer in scientific notation, so let’s just check that this is in scientific
notation. Well, because two is between one
and 10 and our exponent, two, is an integer, this answer is in scientific
notation. So, this is our final answer.