Question

How do the laws work with rational exponents? Provide the class with a third expression to simplify that includes rational (fractional) exponents.

Answer 1

they work the same way as they do with integer exponents

Answer 2

\[16^{\frac{1}{4}}\times 16^{\frac{1}{2}}=16^{\frac{1}{4}+\frac{1}{2}}=16^{\frac{3}{4}}=\sqrt{16^3}=2^3=8\]

Answer 3

and since
\[16^{\frac{1}{4}}=\sqrt[4]{16}=2\] and
\[16^{\frac{1}{2}}=\sqrt{16}=4\] is as a good thing that
\[2\times 4=8\]