This is everything I know about exponents, explained with the Prescribed Learning Outcomes, even numbers only. Odd numbers are on the link below.

2) Describe how powers represent repeated multiplication.

This means that the student must represent powers as repeated multiplication. For example, 1⁴ is equal to 1x1x1x1, because power is essentially a shortcut for repeated multiplication.

4) Demonstrate the difference between two given powers in which the exponent and the base are interchanged using repeated multiplication, such as 2^3 and 3^2

The reason why this is a Prescribed Learning Outcome is because there is a common misconception which the exponents are another way to write multiplication like 2×3, which, for them means that 3×2 is the same thing. But its not, because exponents are repeated multiplication, not regular multiplication. For example, 2³ and 3² are not the same, because written out they say 2x2x2 and 3×3, which is 8 and 9, and obviously, 8 is not equal to 9

6) Explain the roles of parenthesis in powers by evaluating a given set of of powers such as (-2)⁴, (-2⁴), and -2⁴.

If there is an exponent on the outside, than it would be like (-2)(-2)(-2)(-2). If the exponent is in the inside, than it would say (-1)(2)(2)(2)(2). If there are no brackets, than it would say (-1)(2)(2)(2)(2).

8) State the exponent laws for raising a product and quotient to an exponent, explaining the why rules work.

The law for raising a product is (a*b) ^x= a^x * b^x = a^xb^x. Here is the mathematical reasoning:

(a*b) ^x =  (x transfers to both a and b)

a^x * b^{x =} (Now multiply the coefficients)

a^xb^x (Final answer)

 

Here’s an example:

(3*4)²

4²*3²   

12²

144 (final answer

The law for raising a quotient is (a/b) ^x = (a^x)/(b^x) Here is the mathematical reasoning:

(a/b)^x (x transfers to both a and b)

(a^x)/(b^x) (final answer, simplify if possible)

 

Here is an example:

(5/4)²

(5²/4²)

(25/16)

10) State the law for powers with negative exponents and explain why it works.

The negative exponent law is (a)^-x = 1/(a^x), which a cannot be 0. Here is the mathematical reasoning:

5⁰ = 5¹ * 5^-1 = 1

5 * 5^-1 = 1 (divide both sides by 5)

5^-1 = 1/5

12) Use the order of operations to evaluate expressions with powers with integral bases and integral exponents

BEDMAS is very important, as it could easily lead to the wrong answer, so the abbreviation BEDMAS stands for:

Brackets

Exponents

Division and Multiplication (Left to Right)

Adding and Subtracting (Left to Right)

An example question for this would be:

(5²)-7+(3³-7)

25-7+(27-7)

18+20

38

 

14) Identify the error in applying the order of operations in evaluating an expression involving powers.

As said above, the error is usually not following BEDMAS, which is the main reason why people. But, another common error which I haven’t explained yet is how people sometimes treat exponents like multiplication, like 3² for them is 6 when it is really 9.

16) I can identify when it easier to use BEDMAS or to use the exponent laws when evaluating an expression using powers and when they both are a good choice.

This learning outcome is important because it shows people to do things more effectively, without having to calculate large exponents that may be hard to calculate. There isn’t much to explain, but usually the bigger the power, like 3¹⁰ / 3⁸, you should probably do exponent laws first, because no one doesn’t want to multiply 3 ten times and than dividing it by 3 to the power of 8.

18) Use powers to solve problems (measurement problems)

An example of this is when you are trying to find the area a of square, with a side length of 7. Since it is a square, you can square the side length, which becomes 7², which equals to 49.

 

Partner’s link: https://myriverside.sd43.bc.ca/nathanielh/2025/10/08/eveything-i-know-about-exponents/