If a, b, c and d are positive integers such that $${{\mathtt{a}}}^{{\mathtt{b}}}{\mathtt{\,\times\,}}{{\mathtt{c}}}^{{\mathtt{d}}} = {{\mathtt{2}}}^{{\mathtt{10}}}{\mathtt{\,\times\,}}{{\mathtt{7}}}^{{\mathtt{9}}}$$, what is the least possible value of a + b + c + d ?

Guest May 3, 2015

#3**+10 **

Best Answer

2^{10} is 2^{1}*2^{9} so I just combined the 2^{9} with the 7^{9} to get 14^{9}

I couldn't see any other combination giving a lower result (the original expression results in a sum of 28), though I guess I haven't actually *proved* that 26 is the smallest possible value.

.

Alan May 4, 2015