# Indices question!

#### caramelcake

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.

#### skeeter

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

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

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

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

finish up by equating exponents

• caramelcake

#### caramelcake

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

MHF Helper
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.

• caramelcake

#### daniel123

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

#### eumyang

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