Math-2 Lesson 5-2 Properties of Exponents part 2

Quiz 7-1: 1.2.

Citizenship Whose job is it to pick up the trash?

Quiz:

Properties of Exponents Power: An expression formed by repeated Multiplication of the same factor. coefficient Base Exponent

Negative Exponent Property “Grab and drag” When you “Grab and drag” the base and its exponent across the “boundary line” between numerator and denominator, you just change the sign of the exponent. Why do we call this the negative exponent property?

Negative Exponent Property Possible errors When you “Grab and drag” the base and its exponent across the “boundary line” between numerator and denominator, you just change the sign of the exponent. DO NOT GRAB the coefficient!

Negative Exponent Property Possible errors When you “Grab and drag” anything across the “boundary line” between numerator and denominator, you just change the sign of the exponent. What is the exponent of the number 4? Which of these is correct?

Examples:

Your Turn:

Quotient of Powers This is really a silly property. We don’t even need to memorize this as a separate property. It’s just the negative exponent property.

Examples:

Examples: (power of a power property) CAREFUL!! The base for exponent 4 is just the numerator!

Examples: “Grab and drag” Product of powers: add the exponents of same based powers

Your Turn:

Do you “ grab and drag (up or down)?? Product of powers property: add the exponents of like-based powers Make sure when you’re all done, there are NO NEGATIVE EXPONENTS remaining. It doesn’t matter!!!!

Power of a Quotient Property General form of Power of a quotient: This is another silly property. Isn’t it just repeated multiplication of the same factor?

Power of a Quotient Property General form of Power of a quotient: This is another silly property. Isn’t it just the power of a power property?

Your turn: Explain, in your own words, what the negative exponent property allows you to do with powers. Include in your answer the words: “base,” “exponent” “numerator” and “denominator”.

Your Turn: Remember: if you don’t see an exponent, what is the exponent?  (1)

Zero Exponent Property Any base raised to the zero power simplifies to one.

Examples:

Your Turn:

Vocabulary Scientific Notation: used for VERY small or VERY large numbers. VERY large numbers. (microscopically small or galaxy huge). (microscopically small or galaxy huge). Format: Where ‘c’ is ± a decimal number that is between 1 and 10 (3.79, 4.533, 2.0, etc.) and ‘n’ is an integer (2, 5, -9, -3, 25, etc.) ‘n’ is an integer (2, 5, -9, -3, 25, etc.) Example:

Converting to Exponential Notation. How do you write the following number in exponential notation? notation? Start counting “places” from the decimal point until you reach the place right before the last number on the left  14 places

Converting to Exponential Notation. How do you write the following number in exponential notation? notation? Count the number of “places” from the decimal point to the right side of the first number. Very small number  negative exponent on the 10  1/10 to the 8 th power. exponent on the 10  1/10 to the 8 th power  8 places

Your Turn: Convert to exponential notation: Convert to exponential notation:

Converting from Exponential Notation. How do you write the following number in as a regular number? Exponent is a positive number  a big number. Move the decimal 7 spaces to the right.

Converting from Exponential Notation. How do you write the following number in as a regular number? Exponent is a negative number  a small number. Move the decimal 5 spaces to the left.

Your Turn: Convert to exponential notation: Convert to exponential notation:19.20.