Question 1135965
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{{{25*125^(2r) = 25^(3r+3)}}}<br>
(1) Usually when an exponent in an equation is of the form ax+b, it is going to help if you separate the expression into two parts.  In your example, rewrite "25^(3r+3)" as the product of 25^(3r) and 25^3.
{{{25*125^(2r) = 25^3*25^(3r)}}}<br>
(2) The bases for the exponents are 125 and 25, which are both powers of 5.  So rewrite the equation using 5 as the base for the exponents.
{{{25*(5^3)^(2r) = 25^3*(5^2)^(3r)}}}<br>
{{{25*5^(6r) = 25^3*5^(6r))}}}<br>
And now we have a problem.  5^(6r) is a positive number, so we can divide both sides of the equation by it to get<br>
{{{25 = 25^3}}}<br>
That is clearly false; that means the original equation has no solution.