jmc

Question

Evaluate [3]12 [3]20 [3]15 [3]60.

Accepted Answer

We have align* &[3]12 [3]20 [3]15 [3]60 &=[3]2^2 3^1 [3]2^2 5^1 [3]3^1 5^1 [3]2^2 3^1 5^1 &=[3](2^2 3^1)(2^2 5^1)(3^1 5^1)(2^2 3^1 5^1) &=[3](2^2 2^2 2^2)(3^1 3^1 3^1)(5^1 5^1 5^1) &=[3](2^6)(3^3)(5^3) &=[3]2^6[3]3^3 [3]5^3 &=(2^2)(3)(5) = 60. align*