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Chapter 5: Problem 58
Find each product. $$\left(x^{2}+y\right)\left(x^{2}-y\right)$$
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Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.
In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{20 x^{7} y^{4}-15 x^{3} y^{2}-10 x^{2} y}{-5 x^{2} y}$$
In Exercises \(79-82,\) simplify each expression. $$\frac{2 x^{3}(4 x+2)-3 x^{2}(2 x-4)}{2 x^{2}}$$
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. The Washington Monument, overlooking the U.S. Capitol, stands about 555 feet tall. Stacked end to end, how many monuments would it take to reach 1.35 trillion feet? (Note: That's more than twice the distance from Earth to the sun.)
Explain how to simplify an expression that involves a quotient raised to a power. Provide an example with your explanation.
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