91Ó°ÊÓ

Simplify each radical. Assume that all variables represent nonnegative real numbers. $$ \sqrt{a^{13}} $$

If an investment of \(P\) dollars grows to \(A\) dollars in 2 yr, the annual rate of return on the investment is given by $$ r=\frac{\sqrt{A}-\sqrt{P}}{\sqrt{P}} $$ First rationalize the denominator, and then find the annual rate of return (as a percent) if \(\$ 50,000\) increases to \(\$ 54,080.\)

Simplify each expression. $$\left(2 x^{3}\right)^{-1}$$

Simplify each radical. Assume that all variables represent nonnegative real numbers. $$ \sqrt{81 m^{4} n^{2}} $$

Simplify each radical. Assume that all variables represent nonnegative real numbers. $$ \sqrt{\frac{7}{x^{10}},} x \neq 0 $$

Use a calculator with a cube root key to find each root. Round to the nearest thousandth. $$ \sqrt[3]{-87} $$

Combine like terms. $$ 9 x^{2}+3 x^{2}-2 x+4 x-8+1 $$