91Ó°ÊÓ

Simplify each expression. Assume that all variables represent positive real numbers. $$ -8 y^{11 / 7}\left(y^{3 / 7}-y^{-4 / 7}\right) $$

Simplify. Assume that all variables represent positive real numbers. \(\sqrt[3]{64 a^{15} b^{12}}\)

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.

Find each power of i. $$i^{83}$$

Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. $$ \frac{\sqrt{5}+\sqrt{6}}{\sqrt{3}-\sqrt{2}} $$

The coefficient of self-induction \(L\) (in henrys), the energy P stored in an electronic circuit (in joules), and the current I (in amps) are related by the formula $$ I=\sqrt{\frac{2 P}{L}} $$ Find \(I\) if \(P=120\) and \(L=80\).

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. \(\sqrt[3]{-16 z^{5} t^{7}}\)

Find each power of i. $$i^{-5}$$

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \sqrt[5]{x^{3}} \cdot \sqrt[4]{x} $$