Review Laws of Exponents

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Review 6.1-6.2 Laws of Exponents

LAW #1 Product law: Ex: NOTE: add the exponents together when multiplying the powers with the same base. This operation can only be done if the base is the same! SIMPLIFY THESE ON YOUR OWN:

LAW #2 Power of a power: Ex: NOTE: keep the base and multiply the exponents. Multiply the exponents, not add them! SIMPLIFY THESE ON YOUR OWN:

LAW #3 Power of a product:
Ex: NOTE: Distribute the power to each number or variable in the parentheses. YOU CANNOT DISTRIBUTE THE POWER WHEN YOU ARE ADDING OR SUBTRACTING!! SIMPLIFY THESE ON YOUR OWN:

LAW #4 Quotient Property
NOTE: Ex: This operation can only be done if the base is the same! Subtract “TOP EXPONENT MINUS THE BOTTOM EXPONENT” SIMPLIFY THESE ON YOUR OWN:

LAW #5 Quotient Property
Ex: Distribute the power to the top and bottom of the quotient. SIMPLIFY THESE ON YOUR OWN:

LAW #6 Zero exponent law:
Any power raised to an exponent of zero equals one. SIMPLIFY THESE ON YOUR OWN:

LAW #7 Negative exponents:
NOTE: Ex: This does not change the sign of the base. To make an exponent positive, flip the base. SIMPLIFY THESE ON YOUR OWN:

More examples on your own:

More examples on your own:

More examples on your own:

More examples on your own:

LAW #8 Rational exponents:
NOTE: Ex: The bottom number is your root, and top stays as a power Rewrite these expressions:

Examples:

Examples:

Examples:

Get a common denominator - this is going to be our index
Examples: Simplify each expression Get a common denominator - this is going to be our index

Remember we add exponents
Examples: Simplify each expression Remember we add exponents

Examples: Simplify each expression

Examples: Simplify each expression

Examples: Simplify each expression