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Let's solve the given equation step by step:

We are given the equation:

\[
c^{-6} = \frac{1}{(c^2 + x)^3}
\]

We need to find the value of \(x\).

### Step 1: Rewrite both sides in a similar form
We want to express both sides of the equation as powers of \(c\) so that we can compare the exponents.

On the left-hand side, we already have \(c^{-6}\).

On the right-hand side, let's rewrite the denominator:

\[
\frac{1}{(c^2 + x)^3} = (c^2 + x)^{-3}
\]

Thus, the equation becomes:

\[
c^{-6} = (c^2 + x)^{-3}
\]

### Step 2: Equate exponents
Since both sides have the same base (in this case, the expression \(c\)), we can equate the exponents. This gives us:

\[
-6 = -3 \log_c (c^2 + x)
\]

### Step 3: Solve for \(x\)
\

If c^(-6) = 1/((c^2 + x)^3), then what is the value of x?

Step-by-step solution to find the value of x in the equation c^(-6) = 1/((c^2 + x)^3), involving exponent rules and equating powers. Suitable for high school algebra students.

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