Question

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

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Answer 1

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Answer 2

The required value of $2^{(-a)}\times 7^b\times5^{(-c)}$ is $\frac{7}{200}$.

Step-by-step explanation:

Consider the provided information.

$1960 = 2^a \times 5^b\times 7^c$

First calculate the prime factorization of 1960.

1960 = 2 × 2 × 2 × 5 × 7 × 7 = 2³ × 5 × 7²

Now compare the prime factorization with $2^a \times 5^b\times 7^c$

By the comparison we can concluded that a = 3, b = 1  and c = 2.

Substitute the value of a, b and c in $2^{(-a)}\times 7^b\times5^{(-c)}$

$2^{(-3)}\times 7^1\times5^{(-2)}=\frac{7}{2^3\times5^2}=\frac{7}{200}$

Hence, the required value of $2^{(-a)}\times 7^b\times5^{(-c)}$ is $\frac{7}{200}$.

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