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Chapter 0: Problem 84
Evaluate each expression without using a calculator. $$121^{\frac{1}{2}}$$
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Use Einstein's special-relativity equation $$R_{a}=R_{f} \sqrt{1-\left(\frac{v}{c}\right)^{2}}$$ described in the Blitzer Bonus on page \(47,\) to solve this exercise. You are moving at \(90 \%\) of the speed of light. Substitute \(0.9 c\) for \(v,\) your velocity, in the equation. What is your aging rate, correct to two decimal places, relative to a friend on Earth? If you are gone for 44 weeks, approximately how many weeks have passed for your friend?
Evaluate each expression without using a calculator. $$32^{-\frac{4}{5}}$$
Why must \(a\) and \(b\) represent non negative numbers when we write \(\sqrt{a} \cdot \sqrt{b}=\sqrt{a b ?}\) Is it necessary to use this restriction in the case of \(\sqrt[3]{a} \cdot \sqrt[3]{b}=\sqrt[3]{a b} ?\) Explain.
In Exercises 136鈥�143, determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$4^{-2}<4^{-3}$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$\left(4 \times 10^{3}\right)+\left(3 \times 10^{2}\right)=4.3 \times 10^{3}$$
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