91Ó°ÊÓ

Multiply and simplify. Assume that no radicands were formed by raising negative numbers to even powers. $$\sqrt{5} \sqrt{10}$$

Identify the radicand and the index for each expression. $$ \frac{a^{2}}{b} \sqrt[6]{a(a+b)} $$

The velocity of water flow, in feet per second, from a nozzle is given by $$ v(p)=12.1 \sqrt{p} $$ where \(p\) is the nozzle pressure, in pounds per square inch (psi). Find the nozzle pressure if the water flow is 100 feet per second.

Simplify. Use absolute-value notation when necessary. $$ \sqrt[9]{t^{9}} $$

Laws of Exponents Use the laws of exponents to simplify. Write answers using exponential notation, and do not use negative exponents in any answers. $$5^{1 / 4} \cdot 5^{1 / 8}$$

Laws of Exponents Use the laws of exponents to simplify. Write answers using exponential notation, and do not use negative exponents in any answers. $$\left(5^{5 / 4}\right)^{3 / 7}$$

Laws of Exponents Use the laws of exponents to simplify. Write answers using exponential notation, and do not use negative exponents in any answers. $$\left(64^{3 / 4}\right)^{4 / 3}$$

Perform the indicated operation and simplify. Assume that all variables represent positive real numbers. Write the answer using radical notation. $$ \sqrt{2 x^{3} y^{3}} \sqrt[3]{4 x y^{2}} $$

Simplifying Radical Expressions Use rational exponents to simplify. Write answers using radical notation, and do not use fraction exponents in any answers. $$\sqrt[12]{a^{6}}$$

Radar Range. The function given by $$R(x)=\frac{1}{2} \sqrt[4]{\frac{x \cdot 3.0 \times 10^{6}}{\pi^{2}}}$$ can be used to determine the maximum range \(R(x),\) in miles, of an ARSR-3 surveillance radar with a peak power of \(x\) watts. Determine the maximum radar range when the peak power is \(5 \times 10^{4}\) watts.