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Chapter 0: Problem 72
Simplify the radical expressions if possible. $$\sqrt[3]{12} \cdot \sqrt[3]{4}$$
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Simplify using properties of exponents. $$\left(x^{\frac{2}{3}}\right)^{3}$$
Perform the indicated operations. $$ \left(x^{n}+2\right)\left(x^{n}-2\right)-\left(x^{n}-3\right)^{2} $$
Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{\frac{1}{2}} y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}}\right)^{-4} $$
Simplify using properties of exponents. $$\left(25 x^{4} y^{6}\right)^{\frac{1}{2}}$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Suppose a square garden has an area represented by \(9 x^{2}\) square feet. If one side is made 7 feet longer and the other side is made 2 feet shorter, then the trinomial that models the area of the larger garden is \(9 x^{2}+15 x-14\) square feet.
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