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# MATHCOUNTS Question

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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
+26322
+10

210 is 21*29 so I just combined the 29 with the 79 to get 149

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.

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Alan  May 4, 2015
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#1
+26322
+10

a=2, b=1, c = 14, d = 9

210*79 = 21*149

a + b + c + d = 26

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Alan  May 4, 2015
#2
+90968
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How did you do this Alan?

Melody  May 4, 2015
#3
+26322
+10

210 is 21*29 so I just combined the 29 with the 79 to get 149

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

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