Powers: Reverse Rules - Raising a Power to Another Power
Which of the following has the same value as $$5^6$$?
Correct.
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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.
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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.
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Incorrect.
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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.
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Eliminate this answer choice since it is not a power of only 5.
>$$250^3 = (25 \cdot 10)^3 = (5 \cdot 5 \cdot 5 \cdot 2)^3$$
$$30$$
$$25^2$$
$$50^3$$
$$125^2$$
$$250^3$$
