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Chapter 5: Problem 164
The mad Dr. Frankenstein has gathered enough bits and pieces (so to speak) for \(2^{-1}+2^{-2}\) of his creature-to-be. Write a fraction that represents the amount of his creature that must still be obtained.
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We have seen that in \(2009,\) the United States government spent more than it had collected in taxes, resulting in a budget deficit of \(\$ 1.35\) trillion. a. Express 1.35 trillion in scientific notation. b. Express the 2009 U.S. population, 307 million, in scientific notation. c. Use your scientific notation answers from parts (a) and (b) to answer this question: If the 2009 budget deficit was evenly divided among every individual in the United States, how much would each citizen have to pay'? Express the answer in scientific and decimal notations.
Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\frac{\left(2^{1} x^{3} y^{-1}\right)^{-2}\left(2 x^{6} y^{4}\right)^{-2}\left(9 x^{3} y^{3}\right)^{0}}{\left(2 x^{4} y^{6}\right)^{2}}$$
Use a vertical format to find each product. $$\begin{array}{r}9 y^{3}-7 y^{2}+5 y \\\3 y^{2}+5 y \\\\\hline\end{array}$$
In Exercises \(79-82,\) simplify each expression. $$\frac{2 x^{3}(4 x+2)-3 x^{2}(2 x-4)}{2 x^{2}}$$
Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)+(y-1)\left(y^{2}+y+1\right)$$
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