If 3x-y=12, what is the value of (8 ^(x) )/(2^(y) ) A) 2^12 B) 4^4 C) 8^2 D) The value cannot be determined for the information​

Question

If 3x-y=12, what is the value of


`(8 ^(x) )/(2^(y) )`
A) 2^12
B) 4^4
C) 8^2
D) The value cannot be determined for the information​

Answer 1

2¹² (Option A)

Explanation:

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FACTS TO KNOW BEFORE SOLVING :-

• Any number having 0 as its exponent , the overall result will be 1. For e.g. :-
  `a^0 = 1` (where 'a' is any number).

• Lets say there's a number 'a' having '- x' as its exponent , then -
  `(1)/(a^(-x)) = a^x`

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Lets put random values in place of x.

Let x be 0.

Putting x = 0 in the eqn. 3x - y = 12 gives the value of y.

`=> 3 * 0 - y = 12`

`=> -y = 12`

`=> y = -12`

So, we can conclude that by putting x = 0 , we get y = -12.

Now , putting x = 0 & y = -12 in
`(8^x)/(2^y)` gives -

`=> (8^0)/(2^(-12)) = (1)/(2^(-12)) = 2^(12)`