Brandon Henricksen   Block B, Ms. Hubbard

 

• Represent repeated multiplication with exponents

We use exponents to write out equations faster and easier

Eg: 10⁵= 10 x 10 x 10 x 10 x 10 = 100 000

Describe how powers represent repeated multiplication

 

The power are the numbers that are being multiplied

Eg: 10⁵= base x base x base x base x base= product

• Demonstrate the difference between the exponent and the base by building models of a given power, such as 2³ and 3².

 

In the equation= 2^3, the 3 represents that it’s a cube, and the 2 is the length, height, and width of the cube and therefore also equals how many squares on in each face if you see it that way.

         . Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication, such as 2³ and 3².

2^{^3}is 2 x 2 x 2 its 2 multiplied by itself 3 times. While 3^2 is 3 x 3, 3 multiplied by itself 2 times

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

(-5)^2 would be 25 because if the exponent is an even number the answer is positive

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

The parentheses are to tell you what the answer is going to be for example if you have -2^4 when you turn it into a extended answer it is -1 x 2 x 2 x 2 x 2 as for (-2^4) would be 16 because it is even but (-2)^4 is -16 because it is multiplying

• Explain the exponent laws for multiplying powers with the same base.

When you are multiplying, and the bases are the same, you add the exponents

Ex:

 

         . Explain the exponent laws for dividing powers with the same base

When you are dividing and the bases are the same subtract the exponents

Ex: x^5 / x^2 = x^3

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

(2a)⁴  =  (2a)(2a)(2a)(2a)  =  (2 • 2 • 2 • 2)(a • a • a • a) = (2⁴)(a⁴) = 16a⁴

        You multiply both 2 and a

Voilà…

 

Explain the law of powers with an exponent zero

 

Any number except zero raised to an exponent of zero equals 1

Ex: 5⁰= 1, 10002130194321743^0 = 1

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

When you have a negative exponent, it is equal to 1/ the base to the positive exponent, so in your case, 17^(-5) = 1/(17^5). Plus, we know that when we multiply to exponents of the same base together, the new exponent is the sum of the two exponents on the left. So 17^4 * 17^9 = 17^(9+4) = 17^13 If we had 17^5 * 17^(-5), we get two results:  we get that this = 1 because any number divided by itself is 1.
we get that this = 17^0 because 5-5 = 0.
So we combine these two and find that 17^0 = 1.

• I can apply the laws of exponents

 

Exponents is however many times the base number must be multiplied by itself

Ex: 10^4 = 10 x 10 x 10 x 10

• I can identify the error in a simplification of an expression involving powers

 

INCORRECT = 5^2 x 5^3 = 5^2×3 = X

CORRECT= 5 ^2 x 5^3 = 5^2+3 = 5^5 = 3,125

• Use the order of operations on expressions with powers

2 + 6 (3 + 1)^2

2 + 6 (4)^2

2 + 6 (16)

2 + 96

= 98

 

Brackets first, so you’d figure out 3 squared, and then you’d multiply that by itself four times.

• Determine the sum and difference of two power

The sum of any two terms multiplied by the difference of the same two terms is easy to find and even easier to work out — the result is simply the square of the two terms. The middle term just disappears because a term and its opposite are always in the middle.

• If you encounter the same two terms and just the sign between them changes, rest assured that the result is the square of those two terms. The second term will always be negative, as in the example,
• Example: (x– 4)(x + 4)

 

• Identify the error in applying the order of operations in an incorrect solution

 

INCORRECT= 5 x (2^2) + 3 x 2 = 46 The person did not use BEMDAS correctly

CORRECT= 5 x (2^2) + 3 x 2 =

• Use powers to solve problems (measurement problems)

If a lego has a total area of 100cm^2 what are the measurements?         

25cm + 25cm + 25cm + 25cm = 100cm^2 or 25^2 + 25^2 = 100cm^2 

• Use powers to solve problems (growth problems)

 

If the amount of people currently online are 10 but they double every hour how many will we have in

3 hours:                                         6 hours:                                     10 hours:

20 x 3 = 60                              240 x 2 = 480                              3840 x 2 = 7 680

60 at 3 hours                                 480 at 6 hours                        7 680 at 10 hours