( 1/4 )^(x−2)=16

is x =8

Font garbling, but

(1/4)^(-2) = 16

8 (2/x) =4

I was so confused of this one that i used the calculator, but the calculator says that x=4. The thing is that my teacher said that 4 is wrong and when i replaced the x with a 4 in the calculator (8 2/4=4) it said that 8 2/4 is not = to 4. I know that but i tried it anyways.
can you guys help me.
plz dont forget to explain+give answer
:), :D

sorry about that

it was actually ( 1/4 )^(x−2)=16

so, for the 1st problem, x-2 = -2

8 = 2^3, so 2=8^(1/3)
4 = 2^2
so, 2^2 = (8^(1/3))^2 = 8^(2/3)

That means 2/x = 2/3 and x=3

To determine if x = 8 is a solution to the equation (1/4)^(x-2) = 16, we need to substitute x = 8 into the equation and check if both sides of the equation are equal.

Substituting x = 8 into the equation:
(1/4)^(8-2) = 16

Simplifying the exponents:
(1/4)^6 = 16

To compare the two sides of the equation, we need to express them with the same base. In this case, we can convert 16 to a power of 1/4.

16 can be written as 4^2:
(1/4)^6 = (4^2)

Now, we can compare the exponents:
(1/4)^6 = 4^(2)

Since the bases (1/4 and 4) are reciprocals of each other, we can conclude that the exponents are also reciprocals of each other.

Therefore, we have:
6 = 2

6 is not equal to 2, which means that x = 8 is not a solution to the equation.

Therefore, x = 8 is not the correct value for x in the equation (1/4)^(x-2) = 16.