* *

**1. Represent repeated multiplication with exponent**

If you had a question that asked you what is equal to that’s just a more difficult way of saying . its a form of .

**2.Describe how powers explain multiplication**

**3. Demonstrate the difference between the exponents and the base by building models of a power.**

**4. Demonstrate the difference two given powers in which the exponent and the base are interchanged by using repeated multiplication**

**5. Explain the role of parentheses in powers**

**6. Evaluating exponents with integral bases and whole number exponents**

When we are doing exponents with negative bases remember that if the exponent is **even** the answer will be **positive** and if it’s **odd** then the answer is **negative**. This rule only works for negative exponents inside parentheses. an example of this is:

= 81

= -27

= -81

= -27

**7. Explain the exponent law for multiplying and dividing powers with the same base.**

When 2 powers have the same base, their exponents can be manipulated before you solve for the power. the 2 laws here are the , and the .

The product law is when both power’s bases are the same, you can add the exponents so would be equal to .

The quotient law is when both powers have the same bases, their exponents can be subtracted would be equal to

**8. explain the law of raising a power to an exponent**

if you get a question that looks like this . this means you have to use the . the power law says that if you an exponent outside parentheses containing a power, then you can **keep the base and multiply the exponents**, so would be equal to .

**9. explain the exponent law for raising a quotient and a product to an exponent.**

the quotient law and product law are above but here they are again,

The product law is when both power’s bases are the same, you can **add the exponents** **and then multiply the** (if there are any) so would be equal to .

The quotient law is when both powers have the same bases, their **exponents can be subtracted, then divide the coefficients** (if there are any)** ** would be equal to

here is an example:

first you would add the exponents from 3 to the power of 4 and 3 to the power of 5,then subtract the exponents from 3 to the power of 7. this gives you . notice how the base didn’t change throughout the whole thing.

**10. explain the law for powers with the exponent of zero**

first any base with an exponent of 0 is equal to 1. this works because while = 1 may not make sense at first there is a way to prove it. if you use PEDMAS the in the expression

= which is 1.

so if is the same thing, the logically its equal to 1

**11. use patterns to explain the zero law**

observe:

= 32

= 16

= 8

= 4

= 2

= 1

**12. Identify the error in the simplification of an expression using exponents**

**13.apply the laws of exponents**

**14. use order of operations on expressions with powers.**

**15. identify the sum and difference of 2 powers**

**16. identify the error in applying the order of operations with the incorrect solutions**

**17 and 19. use powers to and order of operations to solve problems(growth)**

*for the next 2 questions, a) is the powers problem and b) is the order of operations and powers part*

**write an expression using powers to solve the problem, then solve it.**

**18 and 20. use powers and order of operations to solve problems(measurement)**

**problem, write an expression using powers to find the area the question asks you for, then solve it.**

**21. apply the exponent laws to with coefficients and variable bases**

**– the product law**

**– the quotient law**

**– the power law**

**– the zero law**

**– the negative law**

**22. explain the negative exponent law and apply it to both integral and variable bases.**

**23. use the order of operation’s on expressions with powers involving negative exponents, and variable bases.**

**-Anything else I know about exponents**

You did a great job on addressing all of the prescribed outcomes for exponents. Your explanations and examples were easy to understand, especially because you added lots of detail in each outcome. It was also made easy to understand you r explanations and examples when you used colours or bold to emphasize the important words. There was an error in 11 (use patterns to explain the zero law). Your explanation was that the numbers descend by 2. But 32 to 16 to 8 to 4 is not descending by 2 it is dividing by 2. Also you didn’t apply the negative exponent law to variable bases in 22, you only explained using integral bases. Other than that I didn’t find any other errors but in 23 I think it would’ve been better to evaluate your order of operations expression by solving and showing each step underneath the expression other than explaining in a paragraph. I thought that your examples in each outcome were well picked out for they really helped with your explanations. I also thought outcome 3 was swell done because you used a long detailed description to help understand the difference between the exponents and the base. Overall I thought your post was very good other than the couple errors.

Hi Adam,

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