Question

How do I simplify rational exponents?
Such as, (16^-3/5)^5/4

Answer 1

keep in mind that \(\bf \large a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}}\qquad \qquad



a^{-{\color{red} n}} = \cfrac{1}{a^{\color{red} n}}\\ \quad \\ \quad \\

\left(16^{-\frac{3}{5}}\right)^{\frac{5}{4}}\implies 16^{-\frac{3}{5}\cdot \frac{5}{4}}\)

Answer 2

that is \(\Large \bf \left(16^{-\frac{3}{5}}\right)^{\frac{5}{4}}\implies 16^{-\frac{3}{5}\cdot \frac{5}{4}}\)

Answer 3

@jdoe0001 Thank you so much, I appreciate your help.

Answer 4

yw