SOLUTION: Hi, I'm stuck on the following problem. Would you help me solve it, please? Directions: Solve the equation and check all proposed answers. {{{ (x-13)^(2/5)=9 }}} I got 256

Don't raise both sides to the 'reciprocal power' ever again. Raise both sides to
the 'denominator power' instead. I know you were taught to raise both sides to
the 'reciprocal power' when you first started taking algebra.  But don't
do that anymore because it sometimes causes you to lose solutions in more
advanced problems like this one which is more advanced than the ones you had
when you learned to use the reciprocal power. Raise both sides to the
denominator power, (the fifth power) not the reciprocal power.





Now use the principle of square roots:



Write 9 as 3²



Multiply the exponents









So there are 2 solutions.

Using the +,





Using the -





That's the other answer.  Don't raise both sides to the reciprocal power
ever again.  Just raise to the denominator power. 

Edwin