Grade 9s are working on evaluating expressions with exponents.  Today we looked at bases that are integers, and fractions.

We look each time to see what the base is, and can show the repeated multiplication.  In the following examples, if there are parentheses surrounding a negative number which is raised to an exponent, that negative number is what is repeatedly multiplied.  If there are no parentheses, the exponent does not affect the negative.  The base is the positive number the exponent touches.  That number is then repeatedly multiplied, and the negative is applied after. We noticed that if the base is negative, and the power is an even number, the answer will always be positive.

We looked also today at the pattern that we see when we have the same base (in this case 2) raised to many different powers.  We made a table, and looked for the patterns.  We made the exponents go all the way into the negative numbers. We explored to see if this is a linear or non-linear pattern, positive or negative, direct or partial.  It turns out to be pretty interesting on a graph. It is positive, non-linear, and partial.  The y intercept (ordonnée à l’origine) is 1 and it will never cross the x axis.  It gets super close to it, but will never reach it.  That means there is an asymptote (something to learn more about in grade 11).

We looked a bit at what an exponent of 0 means.  We arrive at it by creating a division with the same base and same power in numerator and denominator. We know that anything that is the same on top and bottom will divide to make 1.  We also know that with our exponent laws we can subtract the powers in a division question with the same bases.  Using 2 perspectives we get 2 answers which are then equal.

We used similar logic to explain negative exponents.