How do I simplify fully (p^3 x p^4)/p^2?

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At first this looks quite daunting as it combines a number of different indices (powers) and a fraction. 

The rules for indices are just something that you have to learn - so don't worry if you don't know them yet. Once you do, the answer to this problem will be clear. 

First, let's step back from the question and learn the rules:

x^2 x x^4 = x^6 (the indices are added together)

x^8 / x^3 = x^5 (the second index is subtracted from the first)

Remeber that this only works when the base number (in this case 'x') is the same!

Second, let's look at the question. Let's start with the numerator (top) of the fraction. When the base number is the same (in this case 'p') and being multiplied, the indices are added together. So the top of the fracticion can be simplified to get: p^7.

That means we are now left with: p^7/p^2.

Next, we are going to consider how to simplify the fraction. We need to subtract the value of the denominator's index from the numerator's index. Therefore, we are left with p^5. 

And there is your answer! So (p^3 x p^4)/p^2 simplified is p^5.

If you want to practice, try this one: (x^10)/(x^2 x x^6).

Emily R. 13 Plus  English tutor, 11 Plus English tutor, GCSE English ...

About the author

is an online GCSE Maths tutor with MyTutor studying at Oxford, Magdalen College University

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