Expressions and EquationsCommon Core

8.EE.A.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example,

Your Turn!EXAMPLES: Simplify each expression Product Rule: Remember to deal with the coefficients separately. A)

B)

Quotient Rule: Coefficients (numbers) are divided, exponents are subtracted.

C)

D)

Zero Exponent Rule: Anything with an

exponent of zero should be changed to a 1

E)

F)

Negative Exponent Rule: Move ONLY the variable that the exponent is attached to. If it’s outside parentheses, move everything within the parentheses.

G) H) H)

I) J)

Power Rule: If you raise a power to a power, you are multiplying it by itself, therefore, you must raise any coefficient to the power outside the parentheses, and multiply all exponents. K) L)

M) N)

O) P)

8.EE.A.3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3× and the population of the world as 7×, and determine that the world population is more than 20 times larger.

SCIENTIFIC NOTATION. A number is written in scientific notation when it is in the form a x where 110 and is an integer. To change a decimal to scientific notation: Step 1: Count the number N of decimal places that the decimal point must be moved in order to get only one digit (a) in front of the decimal. Step 2: If you had to move the decimal to the left (you started with a large number), then your exponent is positive (a x ). If you had to move the decimal to the right (you started with a decimal), then your exponent will be negative (a x )

Examples: Write the following in scientific notation.

REVERSING THE PROCESS (going from scientific notation to decimal notation): Look at the exponent on the 10. If the exponent is negative, move the decimal N spaces to the left (toward the negative end of the number line). If the exponent is positive, move the decimal N spaces to the right (toward the positive end of the number line).

Examples: Write the following in decimal notation.

MULTIPLYING & DIVIDING WITH SCIENTIFIC NOTATION. Follow the usual rules of exponents, except separate the pieces. Simplify the numbers, then add/subtract the exponents on the 10’s.