Question

The expression

5
12 ⋅ 5−4
5
−7 ⋅ 52
can be rewritten as a single form of 5^n, where n is an integer. Find the value of n.
(A) 1
(B) 2
(C) 3
(D) 4

Answer 1

The expression 512 ⋅ 5−45−7 ⋅ 52 can be simplified to 5^-3.

Step-by-step explanation:

To rewrite the expression 512 ⋅ 5−45−7 ⋅ 52 as a single form of 5^n, we need to simplify each part separately.

1. 512 can be written as (5*2)^2, which is equal to 5^2 * 2^2 = 25 * 4 = 100.
2. 5−45−7 can be rewritten as (5^-4) * (5^-7), which is equal to 1/(5^4) * 1/(5^7) = 1/625 * 1/78125 = 1/48,828,125.
3. 52 can be written as 5^2 = 25.

Now, we can combine these simplified parts:

100 * (1/48,828,125) * 25 = 100/(48,828,125) * 25 = 2500/48,828,125 = 1/19,531,250.

Therefore, the expression can be written as 5^-3, where n is equal to -3.