2 Evaluate the following expressions. Warm - UpEvaluate the following expressions.1.2.Solution: 16Solution: - 8
3 Radicals/ExponentsWhat does it mean when you have a fractions as an exponent? Such as:What this stands for is: the number in the numerator is the power, and the number in the denominator is the radical power.So I could write this in another way like:
4 Write each statement in a different form than given. 1.2.3.
5 What about negative exponents What about negative exponents? Remember negative exponent means your doing the inverse.
6 Write each statement in a different form than given. 1.2.3.
7 Solve the following rational exponential equation: Rational ExponentsSolve the following rational exponential equation:OPTION #1Step 1: Convert from exponent to radical form:Step 2: eliminate the radical:Step 3: Simplify:
8 Solve the following rational exponential equation: Rational ExponentsSolve the following rational exponential equation:OPTION #2Step 1: Raise to the reciprocal power of the original power:Step 2: Simplify:
9 Solving Radical Equations A radical equation is an equation with one or more radicals that have variables in their radicand.Solving Radical Equations StepsStep 1 Isolate the radical on one side of the equation if necessary.Step 2 Raise each side of the equation to the same power to get rid of the radical.Step 3 Solve the equation and check your solution.
10 Solve a radical Equation Write original equation.Cube each side.Simplify.Subtract 7 from each side.x = 10Divide each side by 2.Solution x = 10Check.
11 Try These… 1. SOLUTION: x = 512 2. SOLUTION: x = -9 3.
12 Rational Exponent Example What is the solution of the equationWrite original equation.Divide each side by 3.Raise each side to the power of 3/2.x = 64Simplify.Solution x = 64Check.
13 Solve an equation with a rational Exponent. Write original equation.Add 1 to each side.Raise each side to the power of 4/3.Apply exponent properties.x = 14Solve the equation.Solution x = 14Check.
14 Try These…1.2.3.SOLUTION: x = 25SOLUTION: x = 1SOLUTION: x = 6
15 Solve an equation w/ an extraneous solution Write original equation.Square each side.FOIL the left side and simplify the right.Write in standard form.Factor.x = 7 or x = -2Solve.x = 7 (The -2 is extraneous)Check.
16 Solve an equation with 2 radicals METHOD 1Write original equation.Square each side.FOIL the left side and simplify the right.Isolate the radical.Divide both sides by 2 .Square each side again.Simplify.Write in standard form and factor.x = 2 or x = -1Solve.x = -1 (The 2 is extraneous)Check.
17 Solve an equation with 2 radicals METHOD 2Write original equation.Graph y1 =Graph y2 =Find the point of intersection!You will find that the ONLY point of intersection is (-1, 2). Therefore, -1 is the only solution of the equation.
18 Try These… Solve the equation. Check for extraneous solutions. 1.2.3.SOLUTION: x = 1SOLUTION: x = 0, 4SOLUTION: x = 3
19 Solve radical inequalities Use a graph to solveSOLUTIONStep 1ENTER the function and y = 3 into the graphing calculator.Step 2GRAPH the functions from Step 1.Step 3Identify the x-values for which the graph of lies above the graph of y = 3.SOLUTION: x > 14
20 Solve the following radical inequalities (try by hand) 1.2.SOLUTION: x > 32SOLUTION: x ≥ 16