MHB Simplification of surds and powers

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The discussion revolves around simplifying expressions involving surds and powers, with a user seeking help after arriving at incorrect values for x, y, and z. Another participant suggests a method for handling multiplication of powers and provides a detailed step-by-step solution using index notation. The correct simplification leads to the expression 6√[4]{5^5}. Additionally, there is a recommendation to learn LaTeX for better clarity in mathematical communication. The conversation highlights the importance of proper notation and method in solving such problems.
danielw
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Hi All

I have this problem. My workings are attached.

View attachment 5870

My answer was:

x=4
y=5
z=6

This is wrong. I don't know where I'm going wrong.

I'd be really grateful if someone could help.

Thanks!

Daniel

View attachment 5869
 

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Can't see the image clearly but I think this is what I would do.
For the multiplication portion
[5^(6/24)][(5^(24/5))/(5^5)]
= [5^(6/24)][(5^(24/5))(5^-5)]

Hint: (x^2)*(x^3) =?
vs (x^2)^3?
 
danielw said:
x=4
y=5
z=6

This is wrong.

No, it's correct! I can't make out your working so I'll post mine for comparison:

$$7\cdot\sqrt[12]{5^{15}}-\sqrt[24]{5^6}\cdot\sqrt[4]{5^{24}}/5^5$$

Rewrite in index notation:

$$=7\cdot5^{5/4}-5^{1/4}\cdot5^6/5^5$$

$$=7\cdot5^{5/4}-5^{1/4+6-5}$$

$$=7\cdot5^{5/4}-5^{5/4}$$

$$=6\cdot5^{5/4}$$

$$=6\sqrt[4]{5^5}$$

You might want to consider learning $\LaTeX$. Quote this post to see the code I have used.
 
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