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If 12^-x = 7, what does 12^2x equal?

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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:

User Jason Mock
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