Question

If $2160=2^a.3^b.5^c$, find a, b and c. Hence calculate the value of $3^a\times 2^{-b}\times 5^{-c}$

Answer 1

$2160=2^a\times 3^b\times 5^c$

$2\times 2\times 2\times 2\times 3\times 3\times 5=2^a\times 3^b\times 5^c$

$2^4\times 3^3\times 5^1=2^a\times 3^b\times 5^c$

$2^a\times 3^b\times 5^c=2^4\times 3^3\times 5^1$

We have

A=4, b=3 and c=1

Hence

$3^a\times 2^{-}b\times 5^{-}c=3^4\times 2^{-}3\times 5^{-}1$

$3\times 3\times 3\times 3\times {\frac{1}{2}}^3\times \frac{1}{5}$
$81\times \frac{1}{8}\times \frac{1}{5}$
$\frac{81}{40}$
$2\frac{1}{40}$