Answer:To find the value of 12^2x, we can use the given equation 12^-x = 7 as a starting point.
We can rewrite 12^-x as 1/(12^x) since any number raised to the power of -x is equivalent to the reciprocal of that number raised to the power of x.
So the equation becomes 1/(12^x) = 7.
To find the value of 12^2x, we need to manipulate the equation to isolate 12^2x.
First, let's multiply both sides of the equation by 12^x:
(12^x) * (1/(12^x)) = (12^x) * 7.
The left side simplifies to 1, since (12^x) and its reciprocal cancel each other out.
So we have:
1 = 7 * 12^x.
To find 12^2x, we can rewrite it as (12^x)^2, which means raising 12^x to the power of 2.
Substituting this into the equation, we have:
1 = 7 * (12^x)^2.
Now, let's divide both sides of the equation by 7:
1/7 = (12^x)^2.
To find the value of (12^x)^2, we can take the square root of both sides of the equation:
√(1/7) = √((12^x)^2).
Simplifying, we have:
√(1/7) = 12^x.
Therefore, 12^2x is equal to (√(1/7))^2, which simplifies to 1/7.
Explanation: