Chapter 6.3A, Problem 22A

Determine which fraction in each of the following pairs is greater.

a $\left({\frac{1}{2}}^3\right)\text{or}{\left(\frac{1}{2}\right)}^4$

b ${\left(\frac{3}{4}\right)}^{10}\text{or}{\left(\frac{3}{4}\right)}^8$

c ${\left(\frac{4}{3}\right)}^{10}\text{or}{\left(\frac{4}{3}\right)}^8$

d ${\left(\frac{3}{4}\right)}^{10}\text{or}{\left(\frac{4}{5}\right)}^{10}$

e ${32}^{50}\text{or}{4}^{100}$

f ${\left(-27\right)}^{-15}\text{or}{\left(-3\right)}^{-75}$