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Chapter 0: Problem 98
Write each algebraic expression without parentheses. $$-(-17 y)$$
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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. \(\sqrt{7}+\sqrt{18} \sqrt{7+18}\)
will help you prepare for the material covered in the first section of the next chapter. If \(y=1-x^{2}\), find the value of \(y\) that corresponds to values of \(x\) for each integer starting with \(-3\) and ending with 3 .
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ (-2)^{4}=2^{-4} $$
Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{-\frac{5}{4}} y^{\frac{1}{3}}}{x^{-\frac{3}{4}}}\right)^{-6} $$
a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$\text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. }$$ How old is the son? b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
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