Question

The number ( 1/1008 ) can be expressed as ( 2ᵃ times 2ᵇ times 7ᶜ ). Find the value of ( (a - b - c) ).

a) -3
b) 3
c) 1
d) -1

Answer 1

The number (1/1008) expressed as (2ʳ × 2ᵇ × 7⁼) results in a = -4, b = 0, and c = -1. Calculating (a - b - c) gives us -3, which corresponds to option (a).

Step-by-step explanation:

To express the number (1/1008) as (2ʳ × 2ᵇ × 7⁼), we need to factor 1008 into its prime factors. First, let's find the prime factorization of 1008:

1008 = 2 × 504
1008 = 2 × 2 × 252
1008 = 2 × 2 × 2 × 126
1008 = 2 × 2 × 2 × 2 × 63
1008 = 2 × 2 × 2 × 2 × 7 × 9
1008 = 2⁴ × 7 × 3²

Now, we can express 1/1008 as:

1/1008 = 1/(2⁴ × 7 × 3²) = 2⁻⁴ × 7⁻¹ × 3⁻²

Comparing this with (2ʳ × 2ᵇ × 7⁼), we have:

• a = -4 (exponent of 2)
• b = 0 (since there are no 2ᵇ terms in the factorization, b = 0)
• c = -1 (exponent of 7)

Now let's find the value of (a - b - c):
(-4) - (0) - (-1) = -4 + 1 = -3

Therefore, the correct value for (a - b - c) is -3, which corresponds to option (a).