Which of the following has the same value as $$6^6$$?

Correct.
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Notice that $$36^3 = (6^2)^3 = 6^{2 \cdot 3} = 6^6$$.
Hence, this is the correct answer.

Incorrect.
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Notice that $$36^2 = (6^2)^2 = 6^{2 \cdot 2} = 6^4$$.
Hence, eliminate this answer choice.

Incorrect.
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Notice that $$18^2 = (3 \cdot 6)^2 = 9 \cdot 6^2$$.
Hence, eliminate this answer choice.

Incorrect.
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Notice that $$12^3 = (2 \cdot 6)^3 = 8 \cdot 6^3$$.
Hence, eliminate this answer choice.

Incorrect.
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Notice that $$36=6^2$$. Hence, eliminate this answer choice.

$$36$$

$$12^3$$

$$18^2$$

$$36^2$$

$$36^3$$