Answer:
- (1/27)252^(3/4)
- (1/27)fourth root(252^3)
Step-by-step explanation:
The exponent of 1 can be ignored. This means we're simplifying ...
[tex]\left(\left(\dfrac{3}{4}\right)^{-2}+\dfrac{1}{\left(\dfrac{3}{4}\right)}\right)^{3/4}=\left(\dfrac{16}{9}+\dfrac{4}{3}\right)^{3/4}=\left(\dfrac{28}{9}\right)^{3/4}\\\\=\left(\dfrac{28\cdot9}{3^4}\right)^{3/4}=\boxed{\dfrac{252^{3/4}}{27}}\qquad\text{rational exponent form}\\\\=\boxed{\dfrac{\sqrt[4]{252^3}}{27}=\dfrac{\sqrt[4]{16003008}}{27}}\qquad\text{radical form}[/tex]
