91Ó°ÊÓ

Use a calculator to approximate each radical to three decimal places. $$ -\sqrt{91} $$

Simplify each expression. Assume that all variables represent positive real numbers. $$ \left(\frac{2^{-2} w^{-3 / 4} x^{-5 / 8}}{w^{3 / 4} x^{-1 / 2}}\right)^{-3} $$

Simplify each expression. Assume that all variables represent positive real numbers. $$ p^{2 / 3}\left(p^{1 / 3}+2 p^{4 / 3}\right) $$

Simplify. Assume that all variables represent positive real numbers. \(\sqrt{300 z^{3}}\)

Find each power of i. $$i^{89}$$

Simplify each expression. Assume that all variables represent positive real numbers. $$ 6 a^{7 / 4}\left(a^{-7 / 4}+3 a^{-3 / 4}\right) $$

Find each power of i. $$i^{102}$$

Solve each problem. The time for one complete swing of a simple pendulum is given by $$ t=2 \pi \sqrt{\frac{L}{g}} $$ where \(t\) is time in seconds, \(L\) is the length of the pendulum in feet, and \(g,\) the force due to gravity, is about \(32 \mathrm{ft}\) per sec \(^{2}\). Find the time of a complete swing of a 2 -ft pendulum to the nearest tenth of a second.

Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. $$ \frac{m-4}{\sqrt{m}+2} $$

Simplify. Assume that all variables represent positive real numbers. \(\sqrt[4]{81 t^{8} u^{28}}\)