Students will know what it means for a number to be raised to a power and how to represent the repeated multiplication symbolically.
Students will know the reason for some bases requiring parentheses.
Students use the definition of exponential notation to make sense of the first law of exponents.
Students see a rule for simplifying exponential expressions involving division as a consequence of the first law of exponents.
Students write equivalent numerical and symbolic expressions using the first law of exponents.
Students will know how to take powers of powers. Students will know that when a product is raised to a power, each factor of the product is raised to that power.
Students will write simplified, equivalent numeric and symbolic expressions using this new knowledge of powers.
Students know that a number raised to the zeroth power is equal to one.
Students recognize the need for the definition to preserve the properties of exponents.
Students know the definition of a number raised to a negative exponent.
Students simplify and write equivalent expressions that contain negative exponents.
Students extend the previous laws of exponents to include all integer exponents.
Students base symbolic proofs on concrete examples to show that (x^b)^a = x^(ab) is valid for all integer exponents.