Question

If $1960=$ $2^a\cdot 5^b\cdot 7^c$, calculate the value of $2^{-a}\cdot 7^b\cdot 5^{-c}$.

• A. $a=3,b=1$ and $c=3;\frac{49}{80}$
• B. $a=3,b=1$ and $c=2;\frac{16}{595}$
• C. $a=3,b=1$ and $c=3;\frac{5}{192}$
• D. $a=3,b=1$ and $c=2;\frac{7}{200}$

Answer 1

The correct option is D $a=3,b=1$ and $c=2;\frac{7}{200}$

Given,

$1960=2^a.5^b.7^c$
Now,
$1960=2\times 2\times 2\times 5\times 7\times 7=2^3.5^1.7^2$

Thus, comparing the above two, we get
$a=3$, $b=1$, $c=2$,
Now,
$2^{-a}.7^b.5^{-c}$ $=2^{-3}.7^1.5^{-2}$
$=\frac{1}{8}.7.\frac{1}{25}$ $=\frac{7}{200}$