Prescribed Learning Outcomes for Exponents:

• Represent repeated multiplication with exponents
  • 2X2X2 in repeated multiplication is . When connecting the two together you have to think of it like having 2 by itself and then multiplying it by itself. This is different then regular multiplication in the way that the 3 is just 3 twos.

• Demonstrate the difference between the exponent and the base by building models of a given power, such as and .
  • The difference between the two is that is three sides of two where two is the base and three is the exponent and which has two sides of three where 3 is the base and two is the exponent.
• Evaluate powers with integral bases (excluding base 0) and whole number exponents.
  • -24 and –(2)4 have the same base (2) exponent (4) and a negative sign. The difference between the them is the placement of the brackets. In the first one there are no brackets, which means that there is a negative one that is multiplied to the final number

(-1X2X2X2X2=-16). The second one has brackets that enclose the the base and exponent but not the negative sign. This changes the equation as now instead of it always being a negative number, having 4 negatives it becomes positive. (-2 X -2-2 X -2 =16).

• Explain the exponent laws for multiplying and dividing powers with the same base.
  • When evaluating a problem that requires multiplication and division there is a simple way to tell how many exponents are on the answer. All you have to do is add for multiplication and subtract for division by using 0 pairs.

• Explain the law for powers with an exponent of zero.
  • Exponents with zero are easy to calculate. Just as with a base with two it multiplies by two as it gets bigger, when it goes down it gets cut in half. Since one of every number is that number, the number to the zero exponent is always 1.

• Explain the law for powers with negative exponents.
  • Having negative exponents is the continuation of the last question. When having an equation you can turn your exponent from 2 to the first exponent to ½. When you are doing this you are just finding the opposite.

• I can apply the exponent laws to powers with both integral and variable bases.
  • When they have different bases you have to use bedmas to turn them into regular number. You can also find a common multiple like instead of 4 to the 2 you can put it as 2to the 4

• Use the order of operations on expressions with powers.
  • It can get confusing for me when trying this as it only applies in certain places but normally it applies in questions where you have more than one bracket you have to evaluate. This can get tricky as you also have to remember when not to use it as that can actually make the work harder.

• Identify the error in applying the order of operations in an incorrect solution.
  • I can get lots of problems when I do this as it is one of the last things that I check for but I believe that it is easy to find the errors when using it because when I do it if I check again I can find the mistake.

• Use powers to solve problems (growth problems)
  • Using powers can be greatly useful when describing word problems as it can help make the equation much easier. This can get difficult however because you have to write it correctly to solve the question. In this situation the train doubles every hour so the equation must be 2X2x