Tag Archives: ExponentsHUBBARD2017

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.

4^24^64^8 = 65536 When multiplying keep the base and add the exponents.

4^5 ÷ 4^34^2 = 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)^22^26^6 = 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 3^53^{11} = 177147| 3^6 \div 3^53^1 = 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}