Everything I know about exponents

1) Represent repeated multiplication with exponents

4x4x4x4x4 = 1024 $4^5$ = 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 $3^2$ and $2^3$. $3^2$ Represents SA and $2^3$ 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 $3^2$ and $2^3$.

3 x 3= 9 $3^2$ = 9      2 x 2 x 2 = 8 $2^3$ = 8

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

5 x 5 x 5 x 5 = 625 $5^4$ = 625   4 x 4 x 4 x 4 x 4 = 1024 $4^5$ = 1024

6) Explain the role of parentheses in powers by evaluating a given set of powers such as $(-2)^4$ $(-2^4)$ and $-2^4$ $(-2)^4$ = -2 x -2 x -2 x -2 = 16 $(-2^4)$ = (-1 x 2 x 2 x 2 x 2) = -16 $-2^4$ = -1 x 2 x 2 x 2 x 2 = -16

7) Explain the exponent laws for multiplying and dividing powers with the same base. $4^2$ $4^6$ $4^8$ = 65536 When multiplying keep the base and add the exponents. $4^5$ ÷ $4^3$ $4^2$ = 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 $(6^3)^2$ $2^2$ $6^6$ = 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. $2^4$ = 16 $2^3$ = 8 $2^2$ = 4 $2^1$ = 2 $2^0$ = 1

11) Explain the law for powers with negative exponents.

You would have to flip the number with the negative exponent. $\frac {2^{-1}}{1}$ = $\frac {1}{2^1}$

12) Use patterns to explain the negative exponent law. $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$ $\frac{1}{32}$ 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. $(-2)^3$ = -8| $x^6$

14) I can identify the error in a simplification of an expression involving powers. $4^3$ x $4^4$ = $4^7$ People might mistake the answer to this question as $4^{12}$

15) Use the order of operations on expressions with powers

8 x $3^5$ = 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. $3^6 \times 3^5$ $3^{11}$ = 177147| $3^6 \div 3^5$ $3^1$ = 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. $2^3$ = 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? $3^{10}$ = 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. $a^{-2}$ x ${a}^{-5}$ $\frac{1}{a^2} \times \frac{1}{a^5}$ $\frac {1}{a^7}$

Core Competencies Self-Assessment math-25rmzxd

5 thoughts on “Everything I know about exponents”

1. ethanc2017 says:

Clayton when you read this the div and times are not working… On my page it shows it works. But on here it doesn’t.

2. ethanc2017 says:

Don’t view on this part. Click on “View Original” then you won’t see those div and times.

3. ethanc2017 says:

I looked at Ethan’s Blog. I believe that all of the questions are answered accurately.

Emi Ito (Ethan’s Mom)

4. claytonc2017 says:

First of all, it is easier to read when I click view original, I don’t get the not great and as readable frac_____ (I am not quite sure if you did a typo at the top). There were some questions that you could of put a typed out. There were some questions that I thought you could of explained better. There also were some questions that you may of mistyped. All in all it is pretty good (definitely better than mine). If you just check this again and add a little more detail to some questions it would be perfect and is already pretty close to.

5. thubbard says:

Thanks Ethan, please see your Onenote Notebook for my comments.