91Ó°ÊÓ

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{4 x+4 y}\)

Rationalize the denominator and simplify. All variables represent positive real numbers. \(\frac{\sqrt{7}}{3 \sqrt{2}-5}\)

Change each radical to simplest radical form. \(\frac{6 \sqrt{5}}{5 \sqrt{12}}\)

Simplify each expression. Express final results without using zero or negative integers as exponents. \(\frac{x^{-3} y^{-4}}{x^{2} y^{-1}}\)

Why do we need scientific notation even when using calculators and computers?

Simplify each of the following. Express final results using positive exponents only. For example,\(\left(2 x^{\frac{1}{2}}\right)\left(3 x^{\frac{1}{3}}\right)=6 x^{\frac{5}{6}}\). \(\left(y^{\frac{3}{4}}\right)\left(y^{-\frac{1}{2}}\right)\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{16 x+48 y}\)

For Problems \(63-74\), find the indicated products and quotients. Express final results using positive integral exponents only. \(\left(2 x y^{-1}\right)\left(3 x^{-2} y^{4}\right)\)

Simplify each of the following. Express final results using positive exponents only. For example,\(\left(2 x^{\frac{1}{2}}\right)\left(3 x^{\frac{1}{3}}\right)=6 x^{\frac{5}{6}}\). \(\left(x^{\frac{2}{5}}\right)\left(4 x^{-\frac{1}{2}}\right)\)

Rationalize the denominator and simplify. All variables represent positive real numbers. \(\frac{6}{3 \sqrt{7}-2 \sqrt{6}}\)