Let's evaluate each equation one by one.
A. \( (2^2)^4 = 2^6 \)
Using the power of a power rule, \((a^m)^n = a^{m \cdot n}\):
\((2^2)^4 = 2^{2 \cdot 4} = 2^8\)
Since \(2^8\) is not equal to \(2^6\), this equation is incorrect.
B. \( (3^5)^{-2} = 1/3^{-10} \)
Using the power of a power rule:
\((3^5)^{-2} = 3^{5 \cdot -2} = 3^{-10}\).
Now, \(1/3^{-10} = 3^{10}\) (because \(1/a^{-n} = a^{n}\)).
Since \(3^{-10}\) is not equal to \(3^{10}\), this equation is incorrect.
C. \( (5^3)^6 = 1/5^{18} \)
Using the power of a power rule:
\((5^3)^6 = 5^{3 \cdot 6} = 5^{18}\).
Since \(5^{18}\) is not equal to \(1/5^{18}\), this equation is incorrect.
D. \( (8^3)^2 = 8^9 \)
Using the power of a power rule:
\((8^3)^2 = 8^{3 \cdot 2} = 8^6\).
Since \(8^6\) is not equal to \(8^9\), this equation is incorrect.
After evaluating all equations:
- A is incorrect.
- B is incorrect.
- C is incorrect.
- D is incorrect.
None of the equations are correct.