91Ó°ÊÓ

Simplify each expression. Express final results without using zero or negative integers as exponents. \(\frac{a^{-2}}{a^{2}}\)

Express each of the following in simplest radical form. All variables represent positive real numbers. $$ \frac{5}{\sqrt[3]{9 x y^{2}}} $$

Atomic masses are measured in atomic mass units \(\mathrm{~ ( a m u ) . ~ T h e ~ a m u , ~ ( 1 . 6 6 ) ( 1}\) \(\frac{1}{12}\) the mass of a common carbon atom. Find the mass of a carbon atom in kilograms. Express the result in scientific notation.

Simplify each of the following. Express final results using positive exponents only. $$ \left(3 x^{\frac{1}{4}}\right)\left(5 x^{\frac{1}{3}}\right) $$

Change each radical to simplest radical form. \(\frac{3 \sqrt{2}}{4 \sqrt{3}}\)

For Problems \(53-76\), rationalize the denominator and simplify. All variables represent positive real numbers. $$ \frac{\sqrt{3}}{2 \sqrt{5}+4} $$

Simplify each of the following. Express final results using positive exponents only. $$ \left(y^{\frac{2}{3}}\right)\left(y^{-\frac{1}{4}}\right) $$

Simplify each expression. Express final results without using zero or negative integers as exponents. \(\frac{a^{3} b^{-2}}{a^{-2} b^{-4}}\)

Explain why possible solutions for radical equations must be checked.

Express each of the following in simplest radical form. All variables represent positive real numbers. $$ \sqrt{8 x+12 y} \quad[\text { Hint }: \sqrt{8 x+12 y}=\sqrt{4(2 x+3 y)}] $$