## Discussion Forum

### Need help with an AMC8 mock question

Need help with an AMC8 mock question

Let wwxxyy, and zz be whole numbers. If 2^w3^x5^y7^z=5882w⋅3x⋅5y⋅7z=588

then what does 2w+3x+5y+7z2w+3x+5y+7z equal?

(A) 21(B) 25(C) 27(D) 35(E) 56(A) 21(B) 25(C) 27(D) 35(E) 56

Could someone please help explain how to solve this problem? THanks!

Re: Need help with an AMC8 mock question

When I tried to copy and past, it looks normal, but them when I saved it, it is duplicated and formatted weird.

Re: Need help with an AMC8 mock question

What have you tried so far Ashley?

One good place to start is noticing that the powers on the left are all prime numbers. So, how does $588$ look like when you factor it out using prime numbers?

Re: Need help with an AMC8 mock question

2, 3, 5, and 7 are prime numbers. The prime factorization of 588 is 2^2 x 3 x 7^2. 3= 3^1, and since there is no five, you write it as 5^0. 2(2) + 3(1) + 5(0) + 7(2) = 4 + 3 + 0 + 14 = 21, so the answer would be (a) 21.