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6 2 properties of exponents

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This document covers scientific notation and operations with exponents. It defines scientific notation as a number written in the form ab10n, where 1 a < 10 and n is an integer. It provides steps for writing numbers in scientific notation by moving the decimal point and tracking the exponent. Rules are given for multiplying and dividing numbers in scientific notation by combining the coefficients and adding or subtracting the exponents. Examples are provided to demonstrate evaluating numerical expressions using these properties.

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6 2 properties of exponents
Product of Powers Power of a Power Power of a Product Properties of Exponents For each property below: let a and b be real numbers and let m and n be integers.
Negative Exponents Zero Exponent Quotient of Powers Power of a Quotient Properties Cont.
Examples: Evaluating Numerical Expressions:
Evaluate each expression: You Try!
A simplified expression contains no negative exponents! Examples: Simplifying Algebraic Expressions
Simplify You Try!
Scientific Notation A number is written in scientific notation when it has the form: where and b is an integer. Example:
Writing in Scientific Notation Move decimal point until it is behind the first non-zero number. The # of spaces moved is the exponent in x 10? If you moved LEFT: exp. is + If you moved RIGHT: exp. is -
Examples: Write in scientific notation: 5400000 0.009 48900
You Try! Write in scientific notation: 0.000216 384000000
Writing in Std. Form Exponent tells how far to move the decimal. For + exponents: move RIGHT For exponents: move LEFT
Examples: Write in Standard Form:
You Try! Write in Standard Form:
Multiplying To multiply: Multiply front numbers Add exponents Rewrite in scientific notation if needed. Example:
Example: Evaluate:
Dividing To divide: Divide front numbers. Subtract exponents. Rewrite in scientific notation if needed. Example:
Example: Evaluate:
You Try! Evaluate:

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6 2 properties of exponents