Ive each equation.
\[
\left(\frac{1}{8}\right)^{3 n}=\frac{1}{2}
\]

Answer

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Answer

Final Answer: \(\boxed{\frac{1}{9}}\)

Steps

Step 1 ：Given the equation \(\left(\frac{1}{8}\right)^{3 n}=\frac{1}{2}\)

Step 2 ：Express both sides with the same base. The base 8 and 2 can both be expressed as powers of 2.

Step 3 ：Rewrite the equation as \(2^{-3*3n} = 2^{-1}\)

Step 4 ：Equate the exponents: \(-3*3n = -1\)

Step 5 ：Solve for n: \(n = \frac{-1}{-3*3} = \frac{1}{9}\)

Step 6 ：Final Answer: \(\boxed{\frac{1}{9}}\)