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Chapter 0: Problem 52
Rewrite each expression without absolute value bars. $$|-203|$$
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Factor and simplify each algebraic expression. $$(4 x-1)^{\frac{1}{2}}-1(4 x-1)^{\frac{3}{2}}$$
Place the correct symbol, \(>\) or \(<,\) in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. a. \(3^{\frac{1}{2}} \quad 3^{\frac{1}{3}}\) b. \(\sqrt{7}+\sqrt{18} \sqrt{7+18}\)
Simplify each expression. Assume that all variables represent positive numbers. $$ \left(49 x^{-2} y^{4}\right)^{-\frac{1}{2}}\left(x y^{\frac{1}{2}}\right) $$
Factor completely. $$(x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}}$$
Factor and simplify each algebraic expression. $$\left(x^{2}+3\right)^{-\frac{1}{3}}+\left(x^{2}+3\right)^{-\frac{1}{3}}$$
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