If 1960 = 2^a.5^b.7^c, calculate the value of 2^-a.7^b.5^-c.

Factorizing 1960, we get :

⇒ 1960 = 2³.5¹.7²

⇒ 2^a.5^b.7^c = 2³.5¹.7²

⇒ a = 3, b = 1 and c = 2.

Substituting values of a, b and c in 2^-a.7^b.5^-c, we get :

$\Rightarrow 2^{-3} \times 7^1 \times 5^{-2} = \dfrac{1}{2^3} \times 7 \times \dfrac{1}{5^2} \\[1em] = \dfrac{1}{8} \times 7 \times \dfrac{1}{25} \\[1em] = \dfrac{7}{200}.$

Hence, 2^-a.7^b.5^-c = $\dfrac{7}{200}$.