Chapter 7 Review

x 0 = 1 Anything raised to the zero power = 1 1.)2.)

Negative Exponents * Switch Levels and then it is positive 1.) 2.) ) If an exponent is negative it is sad where it is so we move it and then it is happy (positive)

Examples 1. x x -3 q 3. x 3 y x 3 y -1 q -7 4x

Evaluating with Exponents Plug in numbers Move negatives Simplify Ex.) x = 2, y = 4, z = -3

Try x = 5, y = -1, z = 6 1.)2.)

Standard to Scientific Notation 1. Find the factor between 1 and Count the movements 3. Write as factor times ten raised to the number of movements

1. ) 3,500 2.).00467

Try 1.) 6,700,000 2.) ) ) 175,000

Scientific to Standard Examples: x x 10 -5

Try x x x x 10 6

To multiply two powers that have the same base add the exponent 1.) 2 6 x 2 4 = 2 (6+4) = ) x 9 x x 7 =

Try 1.) (4 6 )(4 2 ) 2.) (x 9 )(x 3 ) 3.) (8 2 )(8 4 )

Product of Powers Multiply the constants Add the exponents of like variables 1.) 2.) (5x 3 y 2 )(6xy 3 ) =

Try 1.) (3x 6 )(2x) 2.) (4x 3 )(x 2 ) 3.) (9x 4 )(2x 4 )

Simplifying Monomials 1. Multiply and distribute all powers and parentheses 2. Combine like bases 3. Reduce all fractions

Example 1. (1/3xy)(-6y) 2. (2x) 5 (3x 2 )

3. (1/2x 5 y 3 )(2/3xy 7 ) 4. (9x 5 y)(-2x 5 y 9 ) 2

Multiplying Numbers in Scientific Notation 1. Multiply Factors (number) 2. Add exponents 3. Make sure factor is still greater than 1 and less than ten (Put it in the calculator)

Example 1.) (3. 7 x 10 5 )(4.3 x 10 7 ) 2.) (4.9 x 10 4 )(5.6 x ) 3.) (1.2 x 10 6 )(1.1 x 10 6 )

Power of a Power Distribute to all terms! 1.) 2.) (x 3 ) 2 3.) (x 2 y 3 ) 9

Try 1. (x 3 ) 4 2. (x 2 ) (x 3 y 4 ) 4 4. (x 5 ) 15

Power of a Product Distribute the exponent to each number and variable Simplify the number 1.)

Examples 2.) (4x 2 y 6 ) 3 3.) (2a 4 b 7 ) 4

Dividing Monomials When dividing monomials you subtract exponents with like bases. Example:

Examples 1. x 5 2. x 20 x 3 x x 3 y 6 4. z 8 p 9 x 4 y 3 zp 6

When a fraction is in parentheses distribute the exponent to both the top and bottom Example:

Example z pq x 4

Scientific Notation Put in your calculator! Examples: 1.) (3.45 x 10 4 ) x (4.56 x 10 8 ) 2.) (4.11 x 10 5 ) ÷ (3.23 x 10 7 )