91Ó°ÊÓ

Solve the given problems. Without calculating the actual value, determine whether \(10 \sqrt{11}-\sqrt{1000}\) is positive or negative. Explain.

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$3 x^{-1}-x^{-3}(y+2)$$

Express each of the given expressions in simplest form with only positive exponents. $$3 x^{-1}-x^{-3}(y+2)$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. \(\sqrt{98 x^{6} y^{-7}}\)

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. Then verify the result with a calculator. $$\frac{3 \sqrt{7}-12 \sqrt{2}}{15 \sqrt{7}-12 \sqrt{2}}$$

Simplify the given expressions. Express all answers with positive exponents. $$\left(a^{-2}-a^{-4}\right)^{-1 / 4}$$

Solve the given problems. The adjacent sides of a parallelogram are \(\sqrt{12}\) and \(\sqrt{27}\) units long. What is the perimeter of the parallelogram?

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. \(\sqrt{64+144}\)

Simplify the given expressions. Express all answers with positive exponents. $$\left(a^{3}\right)^{-4 / 3}+a^{-2}$$

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