Core Competencies Self-Assessment math-25rmsfi

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.

= -8|

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 = =

Core Competencies Self-Assessment math-25rmzxd