Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1/x-3
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. 2x2/3 - x-1/3 = x-1/3 ( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √x – 1/√x = 1/√x ( )
> Decide which curves are graphs of functions.
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (f (x))
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x) - g(x)
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g (f (x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. 3√ (f (x)g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)/ g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)g(x)]3
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)]3g(x)
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(x) / f (x)
> Sketch the graph of the function. f (x) = 1 / f(x) = x + 1
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x) / g(x)
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 6 / x – 6, g(x) = x – 6 / x + 6
> Use intervals to describe the real numbers satisfying the inequalities. x ≥ -1 and x < 8
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x)g(x)
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-32y-5)3/5
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-27x5)2/3 / x3/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (25xy)3/2 / x2y
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √x (1/4x)5/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-8y9)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (16x8)-3/4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1 / yx-5
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 2x / √x
> Sketch the graph of the function. f (x) = √(x + 1)
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 5 / x – 10, g(x) = x / x + 10
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x2 / x5y
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (3x2 / 2y)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-3x)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-4 / x3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x3 / y-2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. -x3y / -xy
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. -3x / 15x4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (2x)4
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) =-x / x + 3, g(x) = x / x + 5
> Sketch the graph of the function. f (x) = 2x2 - 1
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-3 * x7
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x5 * (y2 / x)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √(1 + x) * (1 + x)3/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x3y5)4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x/y)-2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 / y2)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x3 * y6)1/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-1/2
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x / x - 8, g(x) =-x / x - 4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 * y5)/ xy2
> Sketch the graph of the function. f (x) = x2 + 1
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x1/3)6
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (xy)6
> Use the laws of exponents to compute the numbers. (61/2)0
> Use the laws of exponents to compute the numbers. 74/3 / 71/3
> Use the laws of exponents to compute the numbers. (125 * 27)1/3
> Use the laws of exponents to compute the numbers. (8/27)2/3
> Use the laws of exponents to compute the numbers. 200.5 * 50.5
> Use the laws of exponents to compute the numbers. (21/3 * 32/3)3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = 3 / x – 6, g(x) = -2 / x - 2
> Use the laws of exponents to compute the numbers. 35/2 / 31/2
> Use the laws of exponents to compute the numbers. 104 / 54
> Describe the domain of the function. g(x) =4 / x(x + 2)
> Use the laws of exponents to compute the numbers. (94/5)5/8
> Use the laws of exponents to compute the numbers. 61/3 * 62/3
> Use the laws of exponents to compute the numbers. (31>3 * 31>6)6
> Use the laws of exponents to compute the numbers. 51/3 * 2001/3
> Compute the numbers. 1-1.2
> Compute the numbers. (.01)-1.5
> Compute the numbers. (1/8)-2/3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = 2 / x - 3, g(x) = 1 / x + 2
> Compute the numbers. 4-1/2
> Compute the numbers. (81)0.75
> Compute the numbers. 160.5
> Describe the domain of the function. g(x) = 1 / √(3 – x)
> Compute the numbers. 91.5
> Compute the numbers. (1.8)0
> Compute the numbers. (27)2/3
> Compute the numbers. (25)3/2
> Compute the numbers. 163/4
> Compute the numbers. 84/3
> Graph the following equations. y = -2x + 3
> Compute the numbers. (-5)-1
> Compute the numbers: (.01)-1
> Compute the numbers. (½)-1
> Compute the numbers. 6-1
> Describe the domain of the function. f (t) =1 / √t
> Compute the numbers. (1 / 125)1/3
> Compute the numbers. (.000001)1/3
> Compute the numbers. (27)1/3
> Compute the numbers. (16)1/2
> Compute the numbers. (.01)3
> Use intervals to describe the real numbers satisfying the inequalities. x < 3
> Compute the numbers. -42
> Compute the numbers. (100)4
> Compute the numbers. (.1)4
> Use the quadratic formula to find the zeros of the functions in Exercises 1–6. f (x) = 2x2 - 7x + 6
> Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial. f (x) = 2x5 - 24x4 - 24x + 2
> Describe the domain of the function. f (x) =8x / (x - 1)(x - 2)
