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

If $$25^{3x} < 125^2$$, what is the greatest possible integer value of $$x$$?
Correct. [[Snippet]] Since $$25 = 5 \cdot 5 = 5^2$$, and $$125 = 5 \cdot 5 \cdot 5 = 5^3$$, then $$25^{3x} < 125^2$$ can be expressed as >$$(5^2)^{3x} < (5^3)^2$$ >$$5^{6x} < 5^6$$. Since the bases are the same, ignore the bases and compare the exponents directly. >$$6x < 6$$ >$$x < 1$$ Hence, the largest possible integer value of $$x$$ is 0.
Incorrect. While -2 is a possible integer value for $$x$$, it is not the greatest integer value. [[Snippet]]
Incorrect. Note that the question uses an inequality, not an equation. If you've done your calculation right, $$x$$ cannot equal 1. [[Snippet]]
Incorrect. [[Snippet]]
Incorrect. [[Snippet]]
-2
0
1
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