### Video Transcript

π is a number. Written as a product of its prime factors in index form, π is equal to two squared
multiplied by five multiplied by π₯ to the power of five. Work out five π cubed as a product of prime factors in index form. Give your answer in terms of π₯.

We are told that, as a product β well, remember, that just means to multiply β of
prime factors, π is equal to two squared multiplied by five multiplied by π₯ to the
power of five. This means that π₯ must be a prime number. So weβre going to take the number π, and according to the order of operations,
BIDMAS or BODMAS, we are going to apply the index before then Iβm multiplying it by
five.

Letβs begin by cubing our number. Itβs two squared multiplied by five multiplied by π₯ to the power of five cubed. We can write this slightly differently as two squared cubed multiplied by five cubed
multiplied by π₯ to the power of five cubed.

Remember, when we have brackets in an index problem, we can multiply the powers. So, for example, π₯ to the power of π to the power of π is the same as π₯ to the
power of ππ. This means that two squared cubed can be written as two to the power of six. And π₯ to the power of five cubed can be written as π₯ to the power of 15, since five
multiplied by three is 15.

Next, we need to multiply this number by five. Itβs five multiplied by two to the power of six multiplied by five cubed multiplied
by π₯ to the power of 15. Since multiplication is commutative β that means it can be performed in any order β
we can rewrite this and put the fives next to each other.

Five is five to the power of one. And then we remember that when we multiply two numbers with the same base β thatβs π₯
in this example here β we can add the powers. π₯ to the power of π multiplied by π₯ to the power of π is equal to π₯ to the power
of π plus π. That means that five to the power of one multiplied by five to the power of three
becomes five to the power of four. And we can say that five π cubed is equal to two to the power of six multiplied by
five to the power of four multiplied by π₯ to the power of 15.