1) Represent repeated multiplication with exponents
4x4x4x4x4 = 1024 = 1024
2) Describe how powers represent repeated multiplication
The large number 4 is called the base, and the small number 5 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.
3) Demonstrate the difference between the exponent and the base by building models of a given power, such as and .
Represents SA and Represents Volume
4) Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication, such as and .
3 x 3= 9 = 9 2 x 2 x 2 = 8 = 8
5) Evaluate powers with integral bases (excluding base 0) and whole number exponents.
5 x 5 x 5 x 5 = 625 = 625 4 x 4 x 4 x 4 x 4 = 1024 = 1024
6) Explain the role of parentheses in powers by evaluating a given set of powers such as , and
= -2 x -2 x -2 x -2 = 16 = (-1 x 2 x 2 x 2 x 2) = -16 = -1 x 2 x 2 x 2 x 2 = -16
7) Explain the exponent laws for multiplying and dividing powers with the same base.
x = = 65536 When multiplying keep the base and add the exponents.
÷ = = 16 When dividing keep the base and subtract the exponents.
8) Explain the exponent laws for raising a product and quotient to an exponent.
2 x = x = 4 x 46656 = 186624 When multiplying keep the base and multiply the exponents. If there is a coefficient add the exponent to the coefficient.
9) Explain the law for powers with an exponent of zero.
When a power is raised to a zero exponent, the answer is 1, except when the base is zero
10) Use patterns to show that a power with an exponent of zero is equal to one.
= 16 = 8 = 4 = 2 = 1
11) Explain the law for powers with negative exponents.
You would have to flip the number with the negative exponent. =
12) Use patterns to explain the negative exponent law.
If I was dividing by 2 I wanted to go lower I would do continue the pattern. So it would go 2,4,8,16,32 and so on.
13) I can apply the exponent laws to powers with both integral and variable bases.
14) I can identify the error in a simplification of an expression involving powers.
x = People might mistake the answer to this question as
15) Use the order of operations on expressions with powers
8 x = 1944 First you would do the exponent. So then the question will become 8 x 243 = 1944
16) Determine the sum and difference of two powers.
= = 177147| = = 3
17) Identify the error in applying the order of operations in an incorrect solution.
(10 + 50) x 5 = 260 The correct answer is 300 because you have to do the brackets before the multiplication 60 x 5 = 300
18) Use powers to solve problems (measurement problems)
Find the volume for a cube that is 2 cm in length, width and height. = 8 cm
19) Use powers to solve problems (growth problems)
Bacteria grows very rapidly. start with 1 bacteria and the bacteria multiplies 3 times every 1 hour. how much bacteria will there be in 10 hours? = 59049 There will be 59049 bacteria in 10 hours.
20) Applying the order of operations on expressions with powers involving negative exponents and variable bases.
x = =