91Ó°ÊÓ

Evaluate each of the functions at the given value of \(x\). $$f(x)=x^{100}, \quad x=-1$$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$\left(x^{1 / 3}\right)^{6}$$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$\left(x^{3} \cdot y^{6}\right)^{1 / 3}$$

Use your graphing calculator to find the value of the given function at the indicated values of \(x .\) $$f(x)=\frac{2 x-1}{x^{3}+3 x^{2}+4 x+1} ; \quad x=2, x=6$$

Is the point \((1,1)\) on the graph of the function \(g(x)=(3 x-1) /\left(x^{2}+1\right) ?\)

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$x^{5} \cdot\left(\frac{y^{2}}{x}\right)^{3}$$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$\frac{-x^{3} y}{-x y}$$

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. $$\frac{(25 x y)^{3 / 2}}{x^{2} y}$$

Let \(f(x)=\sqrt[3]{x}\) and \(g(x)=\frac{1}{x^{2}} .\) Calculate the following functions. Take \(x > 0\). $$f(f(x))$$

The expressions may be factored as shown. Find the missing factors. $$\sqrt{x}-\frac{1}{\sqrt{x}}=\frac{1}{\sqrt{x}}(\quad)$$