Nov

2017

## Everything I Know About Exponents

Prescribed Learning Outcomes for Exponents:

1) Represent repeated multiplication with exponents

2) Describe how powers represent repeated multiplications

3) Demonstrate the difference between the exponent and the base by building models of a given power, such as and .

4) Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication, such as and .

5) Evaluate powers with integral bases (excluding base 0) and whole number exponents.

6) Explain the role of parentheses in powers by evaluating a given set of powers such as , and

7) Explain the exponent laws for multiplying and dividing powers with the same base.

8) Explain the exponent laws for raising a product and quotient to an exponent.

9) Explain the law for powers with an exponent of zero.

10) Use patterns to show that a power with an exponent of zero is equal to one.

11) Explain the law for powers with negative exponents.

12) Use patterns to explain the negative exponent law.

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.

15) Use the order of operations on expressions with powers.

16) Determine the sum and difference of two powers.

17) Identify the error in applying the order of operations in an incorrect solution.

18) Use powers to solve problems (measurement problems)

19) Use powers to solve problems (growth problems)

20) Applying the order of operations on expressions with powers involving negative exponents and variable bases.

….Anything else that you know about exponents.

Vocabulary:

Power: an expression made up of a base and an exponent.

Base: the number that gets multipled by itself in a power.

Exponent: however many times you multiply the base by itself in a power.

Integral base: a base that can be negative, positive or even zero.

Variable base: a base that is a letter in which it represents or can replace a number.

Exponential form: a shorter way to write a repeated multiplication.

## ruominz2017

November 15, 2017 at 11:09 pm (3 years ago)Almost all of your explanations are very good. I liked how you used videos to combine talking and writing. They are very detailed. Except there are mistakes on 8 and 9.

For 8: you made a mistake on {4(2^2)^4}

the exponent 4 after 2^2 does not apply to the 4 because it is not outside of the 2 brackets

so the correct answer should be

{4(2^2)^4}

={4(2^8)}

=4*256

=1024

For 9: zero with exponent of zero also equals one

## Kelsey Stewart

November 17, 2017 at 2:51 am (3 years ago)Thank you for your comment Ruo Min. I will be sure to double check my work and fix the errors made.

-Kelsey

## ruominz2017

November 23, 2017 at 5:56 pm (3 years ago)sorry, I was wrong about question 9, 0^0 doesn’t equal one, but I was right about 8

## Curt Stewart

November 17, 2017 at 6:05 am (3 years ago)Kelsey this is all really well done. I really appreciate the way you explain and highlight the key points in each of your lessons. Keep up the good work!

## kelsey2017

November 17, 2017 at 6:41 am (3 years ago)Thank you Dad for taking the time to look through this. I’m so happy to be able to share my work with you through sites such as edublog.