Exponents and Radicals

Evaluate each expression without using a calculator.

(a) \((-3)^{4}\)   (b) \(-3^{4}\)   (c) \(3^{-4}\)   (d) \(\frac{5^{23}}{5^{21}}\) (e) \(\left(\frac{2}{3}\right)^{-2}\)  (f) \(16^{-3 / 4}\)

Simplify each expression. Write your answer without negative exponents.

(a) \(\sqrt{200}-\sqrt{32}\)   (b) \(\left(3 a^{3} b^{3}\right)\left(4 a b^{2}\right)^{2}\)   (c) \(\left(\dfrac{3 x^{3 / 2} y^{3}}{x^{2} y^{-1 / 2}}\right)^{-2}\)