Question

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

• A. $\frac{81}{40}$
• B. $\frac{83}{40}$
• C. $\frac{79}{40}$
• D. $\frac{87}{40}$

Answer 1

The correct option is A $\frac{81}{40}$

We have,
$2160=2^a{.3}^b{.5}^c$
$(2\ast 2\ast 2\ast 2)\ast (3\ast 3\ast 3)\ast 5=2^a{.3}^b{.5}^c$
$\left(2^4\right)\ast \left(3^3\right)\ast 5^1=2^a{.3}^b{.5}^c$
Comparing the exponents of 2, 3, and 5 on both sides, we get
$a=4,b=3$,and $c=1$
Hence, the value
$3^a{.2}^{-b}{.5}^{-c}=3^4{.2}^{-3}{.5}^{-1}=\frac{81}{40}$