1. ## Indices question!

Given that $\displaystyle 10^{2n} \times 5^{4-3n} = 2^x \times 5^y$, express y in terms of n.

Answer: $\displaystyle x = 2n$, $\displaystyle y = 4 - n$
I don't know how to begin, how do I get two answers from one given expression? Sorry if I sound dumb but any help will be greatly appreciated! Thanks in advance.

2. $\displaystyle 10^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y$

$\displaystyle (2 \cdot 5)^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y$

$\displaystyle 2^{2n} \cdot 5^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y$

$\displaystyle 2^{2n} \cdot 5^{4-n} = 2^x \cdot 5^y$

finish up by equating exponents

3. Oh thank you very much skeeter! I haven't really done this sort of sum for a while so I completely forgot about that. Oops.

4. Note that is m and n could be any numbers, there would be an infinite number of solutions. This problem is assuming that m and n are positive integers.

5. Hi im stuck on a question, anyone can help?
simplify
9^-1/2 x 8^2/3

6. (Removed as author of post #5 started a new thread.)