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Chapter 0: Problem 22
Evaluate each exponential expression. $$ \frac{3^{4}}{3^{7}} $$
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ 5^{-2}>2^{-5} $$
What does \(a^{\frac{m}{n}}\) mean?
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?
Will help you prepare for the material covered in the next section. A. Find \(\sqrt{16} \cdot \sqrt{4}\) B. Find \(\sqrt{16 \cdot 4}\) C. Based on your answers to parts (a) and (b), what can you conclude?
Factor and simplify each algebraic expression. $$(x+5)^{-2}-(x+5)^{-2}$$
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