SOLUTION: (1/3)^-3 = 27^-x I do not know how to solve this. Please show me how.

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Question 1035220: (1/3)^-3 = 27^-x I do not know how to solve this. Please show me how.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%281%2F3%29%5E%28-3%29+=+27%5E%28-x%29+
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You can use the rule:
+%28+a%5Eb+%29%2A%28+a%5E%28-b%29+%29+=+a%5E%28%28+b+-+b+%29%29+
+a%5E%28%28+b-b+%29%29+=+a%5E0+
+a%5E0+=+1+
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Multiply both sides by +%281%2F3%29%5E3+
+%281%2F3%29%5E%28-3%29%2A%281%2F3%29%5E3+=+27%5E%28-x%29%2A%281%2F3%29%5E3+
+1+=+27%5E%28-x%29%2A%281%2F3%29%5E3+
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Multiply both sides by +27%5Ex+
+27%5Ex+=+27%5E%28-x%29%2A27%5Ex+%2A%281%2F3%29%5E3+
+27%5Ex+=+1%2A%281%2F3%29%5E3+
+27%5Ex+=+1%2F27+
Multiply both sides by +27%5E1+
+27%5E1%2A27%5Ex+=+1+
+27%5E%28+x+%2B+1+%29+=+1+
+27%5E%28+-1+%2B+1+%29+=+1+
+27%5E0+=+1+
+1+=+1+
So, +x+=+-1+
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check the answer
+%281%2F3%29%5E%28-3%29+=+27%5E%28-x%29+
+%281%2F3%29%5E%28-3%29+=+27%5E%28-%28-1%29%29+
+%281%2F3%29%5E%28-3%29+=+27%5E1+
+%281%2F3%29%5E%28-3%29%2A%281%2F3%29%5E3+=+27%2A%281%2F3%29%5E3+
+1+=+27%2A%28+1%2F27+%29+
+1+=+1+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

(1/3)^-3 = 27^-x I do not know how to solve this. Please show me how. 
%281%2F3%29%5E%28-+3%29+=+27%5E%28-+x%29 

%283%5E%28-+1%29%29%5E%28-+3%29+=+%283%5E3%29%5E%28-+x%29 ------- Changing matrix%281%2C3%2C+1%2F3%2C+to%2C+3%5E%28-+1%29%29, and matrix%281%2C3%2C+27%2C+to%2C+3%5E3%29

3%5E3+=+3%5E%28-+3x%29 

3 = - 3x ------- Bases are equal, and so are their exponents

3%2F%28-+3%29+=+x______highlight_green%28-+1+=+x%29