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Apply fraction cross-multiplication
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$125^{\left(x-5\right)}=5^{\left(2x+1\right)}$
Learn how to solve rational equations problems step by step online. Solve the rational equation 1/(5^(2x+1))=1/(125^(x-5)). Apply fraction cross-multiplication. Decompose 125 in it's prime factors. Simplify \left(5^{3}\right)^{\left(x-5\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals x-5. If the bases are the same, then the exponents must be equal to each other.