1)Represent repeated multiplication with exponents

3⁴=3x3x3x3 Three to the fourth power is the same as saying three times three times three times three because when there is a small number above and to the right, it means the base, (in this case 3) times itself four times.

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

There is a difference between powers in which the exponent and base are the same because a power is not base times exponents, rather base times base continued for the amount of the exponent. Therefore 2³=2x2x2=8 but 3²=3×3=9.

5)Explain the role of parentheses in powers by evaluating a given set of powers such as (-2)⁴, (-2⁴) and -2⁴

For this question, -2 is the base and 4 is the power since -2 is in the brackets but 4 is not. It would be written as (-2)⁴=-2x-2x-2x-2=16. 16 is positive because there are four negative symbols in the expression. For this question, (-2⁴) means the same thing as -2⁴ as the base and exponent are not separate by the brackets. (-2⁴) =-2⁴=-1x2x2x2x2=-16. In this case -16 is negative because we treat the negative symbol as a coefficient of -1 and the base (2) as positive.

 

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

Product law: Keep the base, add the exponents, multiply the coefficients.

Quotient law: keep the base, subtract the exponents, divide the coefficient.

                            

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

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11)Use patterns to explain the negative exponent law.

 When a number has a negative exponent, you must reciprocal the base. This way, the exponent becomes positive.

13)I can identify the error in a simplification of an expression involving powers.

 

 

 

 

15)Determine the sum and difference of two powers.

There are no rules for adding and subtracting exponents, therefore you follow BEDMAS, and do all the exponents first.

 

17)Use powers to solve problems (measurement problems)

Any measurement problem can be written as a power.

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

 

 

The link to my partners blog: https://myriverside.sd43.bc.ca/anitas2019/2019/11/11/everything-i-know-about-exponents/