91Ó°ÊÓ

will help you prepare for the material covered in the next section. In each exercise, use properties of exponents to simplify the expression. Be sure that no negative exponents appear in your simplified expression. $$\frac{32 x^{2}}{16 x^{5}}$$

In Exercises \(137-140\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some irrational numbers are not complex numbers.

will help you prepare for the material covered in the next section. In each exercise, use properties of exponents to simplify the expression. Be sure that no negative exponents appear in your simplified expression. $$\left(x^{-2} y^{3}\right)^{4}$$

What is the meaning of \(a^{-\frac{m}{n}} ?\) Give an example.

Explain why \(a^{\frac{1}{n}}\) is negative when \(n\) is odd and \(a\) is negative. What happens if \(n\) is even and \(a\) is negative? Why?

In simplifying \(36^{\frac{3}{2}},\) is it better to use \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) or \(a^{\frac{m}{n}}=(\sqrt[n]{a})^{m} ?\) Explain.

In Exercises \(137-140\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(\sqrt{x}-7)^{2}=x-49$$

How can you tell if an expression with rational exponents is simplified?

Solve: \(7[(2 x-5)-(x+1)]=(\sqrt{7}+2)(\sqrt{7}-2)\)

In Exercises \(141-143\), perform the indicated operations and write the result in the form \(a+b i\) $$\frac{4}{(2+i)(3-i)}$$