Indices question!

**caramelcake** · May 30th 2010, 05:05 AM

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

Answer: $x = 2n$ , $y = 4 - n$

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.

**skeeter** · May 30th 2010, 06:02 AM

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

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

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

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

finish up by equating exponents

**caramelcake** · May 30th 2010, 06:22 AM

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.

**HallsofIvy** · May 30th 2010, 07:03 AM

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.

**daniel123** · July 18th 2010, 02:20 PM

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

**eumyang** · July 18th 2010, 02:25 PM

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

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