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Chapter 0: Problem 12
Evaluate each expression or indicate that the root is not a real number. $$\sqrt{(-17)^{2}}$$
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In Exercises 136鈥�143, determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$4^{-2}<4^{-3}$$
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 \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
In Exercises 132鈥�135, determine whether each statement makes sense or does not make sense, and explain your reasoning. There are many exponential expressions that are equal to \(36 x^{12},\) such as \(\left(6 x^{6}\right)^{2},\left(6 x^{3}\right)\left(6 x^{9}\right), 36\left(x^{3}\right)^{9},\) and \(6^{2}\left(x^{2}\right)^{6}\)
Simplify by reducing the index of the radical. $$\sqrt[4]{5^{2}}$$
Evaluate each expression. $$\sqrt[3]{\sqrt[4]{16}+\sqrt{625}}$$
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