 Exponent Rules – Day 1 Zero and Negative Exponents.

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Exponent Rules – Day 1 Zero and Negative Exponents

Zero Exponents Anything with an exponent of zero reduces to 1. Examples:

Negative Exponents If an exponent is negative, you can make it positive by moving it. If it is in the denominator, move it to the numerator. If it is in the numerator, move it to the denominator.

Examples

Simplifying Exponents Simplify each exponent

Simplifying Exponential Expressions Simplify each expression

Evaluating an exponential expression Do not forget to follow the order of operations (PEMDAS) Evaluate if:

Examples Evaluate the following expressions if n = -2 and w = 5.

Quick Check: Make sure you understand! Simplify each expression: Evaluate for x = 3, y = -2

Homework! Practice! Study! Big Green pg. 397 (2 - 44 even)

Exponent Rules – Day 2 Scientific Notation

Scientific Notation Rules In the form: n is an integer a is between 1 and 10 Examples:

Scientific Notation or not?

Writing a number in Scientific Notation If the number is very large (>1) the exponent will be positive If the number is very small (<1) the exponent will be negative Why?

Examples 56,900,000 0.00985

Examples 267,000 0.0000325

Writing a number in standard notation

More examples

Ordering Numbers Put the numbers in scientific notation Order the powers of 10 Arrange decimals of the same power of 10 in order Write the original numbers in order

Examples

Multiplying a number in scientific Notation

Examples

Homework! Practice! Study! Big Green pg. 402-403 (2 - 40 even)

Exponent Rules: Day 3 Multiplication Properties of Exponents

Multiplying Powers with the same base If the bases are the same, you can add the exponents. Examples:

More examples

Multiplying Powers in an expression

More Complex Examples

Multiplying Numbers in Scientific Notation

More Examples

Quick Check: Make sure you understand! Simplify:

Homework! Practice! Study! Big Green pg. 407 – 408 (8 - 26 even) (32 - 50 even)

Exponent Rules: Day 4 Dealing with Powers of exponents

Raising a Power to a Power When raising an exponent to an exponent, multiply the exponents together. Example:

More Examples

More Complex Examples

Raising a product to a power Apply the power rule (multiply the exponents) to each factor in the parentheses. Example:

Examples

More Complex Examples

More complex examples

Scientific Notation Examples

More Scientific Notation Examples

Homework! Practice! Study! Big Green pg. 413-414 (2 - 30 even) (42 – 50 even)

Exponent Rules: Day 5 Division Properties of Exponents

The Division Rule When dividing exponents of the same base; subtract the exponents Example:

Examples:

More Examples

Scientific Notation Examples

Raising a quotient to a power Raise everything within the parenthesis to the power! Example:

Examples

More Complex Examples

All Exponent Rules Combined!

Homework! Practice! Study! Big Green pg. 420-421 (10 - 18 even) (30 - 48 even) (52 - 58 even)