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Chapter 0: Problem 44
Factor the difference of two squares. $$36 x^{2}-49 y^{2}$$
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Factor and simplify each algebraic expression. $$\begin{aligned} &x^{\frac{3}{2}}-x^{\frac{1}{2}}\\\ & \end{aligned}$$
In parts (a) and (b), complete each statement. $$\text { a. } b^{4} \cdot b^{3}=(b \cdot b \cdot b \cdot b)(b \cdot b \cdot b)=b^{?}$$ $$\text { b. } b^{5} \cdot b^{5}=(b \cdot b \cdot b \cdot b \cdot b)(b \cdot b \cdot b \cdot b \cdot b)=b^{7}$$ c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?
Simplify by reducing the index of the radical. $$ \sqrt[9]{x^{6}} $$
Determine whether each statement is trueor false. If the statement is false, make the necessary change(s) toproduce a true statement. $$x^{3}-64=(x+4)\left(x^{2}+4 x-16\right)$$
In one short sentence, five words or less, explain what $$ \frac{\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}}{\frac{1}{x^{4}}+\frac{1}{x^{5}}+\frac{1}{x^{6}}} $$ does to each number \(x\).
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