Question 187160
{{{(2/5)^x = 25/4}}}
<pre><font size = 4 color = "indigo"><b>
Since {{{25}}} can be written as {{{5^2}}}
and {{{4}}} can be written as {{{2^2}}},
then {{{25/4}}} can be written as {{{(5/2)^2}}}
Then we can flip the fraction inside the 
parentheses and change the sign of the exponent
and so altogether {{{25/4=(5/2)^2=(2/5)^(-2)}}}.

So now we have

{{{(2/5)^x = (2/5)^(-2)}}}

Now we can equate the exponents since the bases
are the same and positive and {{{""<>1}}}

{{{x=-2}}}

Edwin</pre>