Video Transcript
Simplify six 𝑥 cubed minus three
𝑥 cubed divided by three 𝑥 squared.
Inside our parentheses here, we
have two like terms, two terms that have the same variable taken to the same
power. This means that we can simply
subtract. Six 𝑥 cubed minus three 𝑥 cubed
equals three 𝑥 cubed. In order to divide this value by
three 𝑥 squared though, we’ll need to change a few things. We can keep our first term, bring
down the three 𝑥 cubed. But we need to change our division
to multiplication and take the reciprocal of three 𝑥 squared, which would be one
over three 𝑥 squared. Three 𝑥 cubed times one equals
three 𝑥 cubed. We can add a denominator of one and
then say one times three 𝑥 squared equals three 𝑥 squared.
From here, we notice that three
over three be equal to one, they cancel each other out. And we’re left with 𝑥 cubed over
𝑥 squared. If we drew out 𝑥 cubed and 𝑥
squared, it would look like this. 𝑥 over 𝑥 equals one; they cancel
out. 𝑥 over 𝑥 equals one, and those
cancel out leaving us with 𝑥. But we don’t have to draw them
out. What we can say when we’re dividing
with exponents is that 𝑥 to the third power divided by 𝑥 squared equals 𝑥 to the
three minus two power. We took the power from the
numerator and then you subtract the power of the denominator from the power of the
numerator.
Both options produce the solution
𝑥 to the first power or 𝑥.
