Question

Simplify the expression, ((p^(-2)+1/p)^1 )^p, when p=3/4, in both radical and rational exponents forms.

Answer 1

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 ...

  $\left(\left(\dfrac{3}{4}\right)^{-2}+\dfrac{1}{\left(\dfrac{3}{4}\right)}\right)^{3/4}=\left(\dfrac{16}{9}+\dfrac{4}{3}\right)^{3/4}=\left(\dfrac{28}{9}\right)^{3/4}\\\\=\left(\dfrac{28\cdot9}{3^4}\right)^{3/4}=\boxed{\dfrac{252^{3/4}}{27}}\qquad\text{rational exponent form}\\\\=\boxed{\dfrac{\sqrt[4]{252^3}}{27}=\dfrac{\sqrt[4]{16003008}}{27}}\qquad\text{radical form}$