91Ó°ÊÓ

Express each of the given expressions in simplest form with only positive exponents. $$\frac{a x^{-2}+a^{-2} x}{a^{-1}+x^{-1}}$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. \(\sqrt{b^{4} \sqrt{a}}\)

Simplify the given expressions. Express all answers with positive exponents. $$\frac{3^{-1} a^{1 / 2}}{4^{-1 / 2} b} \div \frac{9^{1 / 2} a^{-1 / 3}}{2 b^{-1 / 4}}$$

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$\frac{a x^{-2}+a^{-2} x}{a^{-1}+x^{-1}}$$

Solve the given problems. For the quadratic equation \(a x^{2}+b x+c=0,\) if \(a, b,\) and \(c\) are integers, the sum of the roots is a rational number. Explain.

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. \(\sqrt{28 u^{3} v^{-5}}\)

Express each of the given expressions in simplest form with only positive exponents. $$2 t^{-2}+t^{-1}(t+1)$$

Simplify the given expressions. Express all answers with positive exponents. $$\left(T^{-1}+2 T^{-2}\right)^{-1 / 2}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. Then verify the result with a calculator. $$\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{6}-4 \sqrt{5}}$$

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$2 t^{-2}+t^{-1}(t+1)$$