### Video Transcript

Simplify seven π₯ to the fourth
power times eight π₯ to the seventh power.

There are two things we know about
multiplication. It is associative and
commutative. The associative property tells us
that the product will be the same no matter how the numbers are grouped. And the commutative property tells
us that the order in which we perform the calculation really doesnβt matter. And so, weβre going to begin by
sort of unsimplifying each term in our expression. When we do, we get seven times π₯
to the fourth power times eight times π₯ to the seventh power. Weβre now going to switch around π₯
to the fourth power and eight. And so, we see that our expression
now becomes seven times eight times π₯ to the fourth power times π₯ to the seventh
power. And in fact, we can work out the
numerical part. We know that seven times eight is
56, which means that this becomes 56 times π₯ to the fourth power times π₯ to the
seventh power.

But what do we do with these
algebraic parts? Well, we have a rule for
multiplying exponential terms. As long as the base is the same, we
add the exponents. So, π₯ to the power of π times π₯
to the power of π is π₯ to the power of π plus π. This in turn means that π₯ to the
fourth power times π₯ to the seventh power is π₯ to the power of four plus
seven. And since four plus seven is 11,
this becomes π₯ to the 11th power. Now, in fact, we know that we donβt
really want to include that multiplication symbol. And so, we simplify this further to
get 56π₯ to the 11th power. And so, when we simplify seven π₯
to the fourth power times eight π₯ to the seventh power, we get 56π₯ to the 11th
power.