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Chapter 0: Problem 103
Simplify by reducing the index of the radical. $$\sqrt[3]{x^{6}}$$
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Explain how to simplify \(\sqrt{10} \cdot \sqrt{5}\)
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(x^{4}-16\) is factored completely as \(\left(x^{2}+4\right)\left(x^{2}-4\right)\)
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?
Simplify using properties of exponents. $$\left(25 x^{4} y^{6}\right)^{\frac{1}{2}}$$
Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime of 80 years. Round the decimal factor in your scientific notation answer to two decimal places.
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