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Chapter 0: Problem 34
Add or subtract terms whenever possible. $$8 \sqrt{5}+11 \sqrt{5}$$
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Simplify using properties of exponents. $$\left(25 x^{4} y^{6}\right)^{\frac{1}{2}}$$
Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)
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?
Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.
Describe what it means to rationalize a denominator. Use both \(\frac{1}{\sqrt{5}}\) and \(\frac{1}{5+\sqrt{5}}\) in your explanation.
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