A problem i found challenging is Dividing Radical expressions. This is one question i struggled solving from making a simple mistake from the rules of exponents.

This is the answer i got my first attempt on solving this expression. These are the steps i did:

1. Finding the common index for 2 and 5, the LCM for 2 and 5 is 10.
2. Express both radicals with the same index. I did that by multiplying 5 to the numerator and 2 to the denominator.
3. Perform the division. I divided the exponents using the laws of exponents.

When i realized my answer was incorrect, i looked up the question on the internet and identified my mistake. The mistake i made was when multiplying the exponents inside the radical. I added the exponents instead of multiplying. I didn’t apply the laws of exponents properly. I applied a^m × aⁿ = a^m+n instead of (a^m)ⁿ = a^mn.

I applied the correct law (a^m)ⁿ = a^mn, and solved the problem correctly like so.

Addition of exponents only apply if the exponent base are the same. The next time i encounter a problem like this, i will be cautious of the different exponent rules and apply it correctly.