Exam 9: Rational Exponents

Combine the complex numbers.

A triangle is equilateral if it has three equal sides. The triangle in the figure is equilateral with each side of length 2 x . Find the ratio of the height to a side.

Refer to the diagram of a square pyramid below. Find the ratio of the altitude a of the pyramid to the height h .

Multiply.

Combine the complex numbers.

Combine the complex numbers.

Use a calculator to find a decimal approximation for Compare it to decimal approximations for and Give answers to three decimal places.

Factor the expression as if it were a trinomial.

Combine the expressions.

Multiply. (Assume the variable represents a nonnegative real number.)

Find the following root, if possible.

Solve the equation. (Hint: square both sides of the equation twice to eliminate the radicals.)

Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

Factor from

Find the following root, if possible.

Solve the equation.

Combine the expressions.

Complex numbers may be applied to electrical circuits. Electrical engineers use the fact that resistance to electrical flow of the electrical current and the voltage are related by the formula . (Voltage is measured in volts, resistance in ohms, and current in amperes). Find the resistance to electrical flow in a circuit that has a voltage volts and current amps.

If you are at a point k miles above the surface of the Earth, the distance you can see (in miles) is approximated by the equation . How far can you see from a point that is 2 miles above the surface of the Earth? Round your answer to the nearest tenth of a mile. __________ miles

Find the product.