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Chapter 0: Problem 26
Find the intersection of the sets. $$\\{0,1,3,5\\} \cap\\{-5,-3,-1\\}$$
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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?
If you are given two real numbers, explain how to determine which is the lesser.
Suppose that a polynomial contains four terms. Explain how to use factoring by grouping to factor the polynomial.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some whole numbers are not integers.
Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{-\frac{5}{4}} y^{\frac{1}{3}}}{x^{-\frac{3}{4}}}\right)^{-6} $$
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