Thread: (2 of 2) Simplifying Expression

1. (2 of 2) Simplifying Expression

Hey guys!

If you’ve read my first post, then this is the second question I thought should be in a new thread.

As stated previously, I’m trying to sharpen my incredibly rusty maths skills in preparation for an OU degree in Autumn, I’ve come across a practise set of questions but I can’t get my head around this one.

The Question:

(5x)^5/4 x^3/2
/
Sqrt 5x^5

Again, I have lots of practise questions similar to these but I just want to get off to the right start.

thanks guys!

2. Re: (2 of 2) Simplifying Expression

This is difficult to understand. Are these two separate expressions? Are they $(5x)^{5/4}x^{3/2}$ and $\sqrt{5x^5}$? If So what is the "/" between them?

Or is this the single problem $\frac{(5x)^{5/4}x^{3/2}}{\sqrt{5x^4}}$? If so why are they on separate lines?

Also what are you supposed to do with them? There is no "problem" without know what you are to do.

If it is $\frac{(5x)^{5/4}x^{3/2}}{\sqrt{5x^4}}$ and the problem asks you to "simplify" or "reduce" them then you need to know a few basic things.
1) $(ab)^n= a^nb^n$ so $(5x)^{5/4}= 5^{5/4}x^{5/4}$.
2) Square root is the 1/2 power: $\sqrt{5}= 5^{1/2}$ and $\sqrt{x^4}= x^{4/2}= x^2$.
3) When you multiply the same base to two exponents, the exponents add: $x^{5/4}x^{3/2}= x^{5/4+ 3/2}= x^{5/4+ 6/4}= x^{11/4}$.
4) When you divide the same base to two exponents, subtract the exponents: $\frac{x^{11/4}}{x^{5/2}}= x^{11/4- 5/2}= x^{11/4- 10/4}= x^{1/4}$.

$\frac{(5x)^{5/4}x^{3/2}}{\sqrt{5x^5}}= \frac{5^{5/4}x^{5/4}x^{3/2}}{5^{1/2}x^{5/2}}= 5^{5/4- 1/2}x^{5/4+ 3/2- 5/2}= 5^{5/4- 4/4}x^{5/4+ 6/4- 10/4}= 5^{1/4}x^{1/4}$

That last can be written as $(5x)^{1/4}$ or $\sqrt[4]{5x}$.