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Chapter 0: Problem 55
Find each product. $$(x-3)^{3}$$
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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 \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
Evaluate each expression without using a calculator. $$8^{\frac{2}{3}}$$
Factor completely. $$ x^{4}-y^{4}-2 x^{3} y+2 x y^{3} $$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ x^{3}-64-(x+4)\left(x^{2}+4 x-16\right) $$
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