Intermediate Algebra for College Students (7th Edition)

$\dfrac{1}{x^{\frac{7}{20}}}$
Use the rule $\dfrac{a^m}{a^n} = a^{m-n}$ to obtain: $=x^{\frac{1}{4} - \frac{3}{5}}$ Make the fraction similar using their LCD of 20 to obtain: $=x^{\frac{5}{20} - \frac{12}{20}} \\=x^{\frac{5-12}{20}} \\=x^{\frac{-7}{20}}$ Use the rule $a^{-m} = \dfrac{1}{a^m}$ to obtain: $=\dfrac{1}{x^{\frac{7}{20}}}$