Question 189523
{{{(1/3)^m=(27)^(m+2)}}} Start with the given equation.



{{{(3^(-1))^m=(27)^(m+2)}}} Rewrite {{{1/3}}} as {{{3^(-1)}}}



{{{(3^(-1))^m=(3^3)^(m+2)}}} Rewrite {{{27}}} as {{{3^3}}}



{{{3^(-m)=3^(3(m+2))}}} Multiply the exponents.



{{{-m=3(m+2)}}} Since the bases are equal, the exponents are equal.



{{{-m=3m+6}}} Distribute.



{{{-m-3m=6}}} Subtract {{{3m}}} from both sides.



{{{-4m=6}}} Combine like terms on the left side.



{{{m=(6)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{m}}}.



{{{m=-3/2}}} Reduce.



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Answer:


So the answer is {{{m=-3/2}}} which in decimal form is {{{m=-1.5}}}.