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# Powers: Reverse Rules - Raising a Power to Another Power

Which of the following has the same value as $$5^6$$?
Correct. [[Snippet]] Some of the answer choices can be eliminated immediately because they contain numbers other than 5. For example, 30 is $$5 \cdot 6$$, so it cannot very well equal $$5^6$$. The only answer choices that are powers of only 5 are B) $$25^2$$ and D) $$125^2$$. Rewrite these answer choices as powers with a base of 5. >$$25^2 = (5^2)^2 = 5^4$$ >$$125^2 = (5^3)^2 = 5^6$$ Since $$125^2$$ is the only answer choice equal in value to $$5^6$$, this is the correct answer.
Incorrect. [[Snippet]] Eliminate this answer choice since it is not a power of only 5. >$$50^3 = (5 \cdot 10)^3 = (5 \cdot 5 \cdot 2)^3$$
Incorrect. [[Snippet]]
Incorrect. [[Snippet]] Eliminate this answer choice for the following reasons: 1) It is too small. >$$5^6 = 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$$ is definitely greater than 30. 2) It includes powers other than 5. >$$30=5 \cdot 6$$, which is definitely not the same as $$5^6$$.
Incorrect. [[Snippet]] Eliminate this answer choice since it is not a power of only 5. >$$250^3 = (25 \cdot 10)^3 = (5 \cdot 5 \cdot 5 \cdot 2)^3$$
$$30$$
$$25^2$$
$$50^3$$
$$125^2$$
$$250^3$$