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Laws of Exponents

Multiplication: xa ( xb = xa + b Ex. x2 ( x5 = x7

Division: xa ÷ xb = xa-b Ex. x8 ÷ x5 = x3

Raising to a Power: (xa)b = xab Ex. (x5)3 = x15

Power of a Product: (xy)a = xa ( ya Ex. (xy)3= x3( y3

Power of a Quotient: [pic] Ex. [pic]

Zero and Negative Exponents

Zero exponents: [pic], so x0 = 1

Negative Exponents:

x-n = [pic]

Fractional Exponents

[pic]

[pic]= [pic]

Solving Equations Involving Exponents

[pic]

Solving Exponential Equations

Solving Exponential Equations with the Same Bases

If the bases are equal, the exponents must be equal.

Ex. Solve for x: 3x = 32x-2

Solving Exponential Equations with Different Bases

If possible, write each term as a power of the same base

Solve for x and check: 22x = 8

Complete the following:

Ex. 1) Write [pic]with only positive exponents.

2) Write the following as a fraction without a denominator: [pic]

3) Write the following with only positive exponents:

a) [pic] b) [pic]

4) Write each of the following without a denominator.

a) [pic] b) [pic]

Evaluate:

1. 32[pic] 2. 81[pic]

3. (-8)[pic] 4. 125[pic]

5. If f(x) = [pic], find f(16).

6. Find the value of 2a0 – (2a)0 + a if a = 64.

To solve an equation involving exponents: Ex.

1. Write the equation with only the variable term 1.

on one side of the equation.

2. Divide both sides of the equation by the coefficient 2.

of the variable term.

3. Raise both sides of the equation to the power that is 3.

the reciprocal of the exponent of the variable.

4. Simplify the right side of the equation. 4.

5. Check the solution.

Example 2 - Solve for x:

Example 3 – Solve for x:

Example 4 – Solve for x:

Ex 2 . Solve for x and check: 5x-1 = 0.04

Ex 3. Solve for a and check: 4a = 8 a +1

Ex 4. Solve for x and check: 3 + 7x-1 = 10

Ex 5. Solve for x and check: [pic]

Ex 6. Solve for x and check: 5x-1 = (0.04)2x

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Laws of Exponents

Zero and Negative Exponents

Fractional Exponents

Solving Equations Involving Exponents

[pic]

[pic]

[pic]

Solving Exponential Equations

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