Aubrey Sparvier
Everything I know about exponents
1)Represent repeated multiplication with exponents: 5x5x5x5=54=625
2)Describe how powers represent repeated multiplication: In the equation above, 5 is the base and 4 is the exponent. The base (5) is the number that you are multiplying and the exponent (4) is how many times you are multiplying the base.
3)Demonstrate the difference between the exponent and the baseby building models of a given power, such as 23 and 32: When drawing a model of a power, the base of the power is the side length of the model and the exponent is the dimension. For 23, the side length would be 2 and it would be in the third dimension. For 32, the side length would be 3 and it would be two-dimensional.
4)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: 23 = 2x2x2 = 9 32 = 3x3 = 9
5)Evaluate powers with intergral bases (excluding base 0) and whole number exponents:14= 1, 23= 8, 33= 27, 46=4096, 53=125
6)Explain the role of parentheses in powers by evaluating a given set of powers such as (-2)4, (-24) and -24: When the exponent is outside the parentheses, (-2)4 , it applies to both numbers ( -1 and 2), when it is on the inside, (-24), it only applies to the two, when there are no parentheses, -24, it’s the same as when the exponent is inside the parentheses.
7)Explain the exponent laws for multiplying and dividing powers with the same base: When you are multiplying powers with the same base, you add the exponents together.
23 x 25 = 23+5 = 28 = 256
When you are dividing powers with the same base, you subtract the exponents.
36 32 = 36-2= 34 = 81
8)Explain the law for raising a product or quotient to an exponent: multiplication: 1) keep the base 2) add exponents 3) multiply coefficients
division: 1) keep base 2) subtract exponents 3) divide coefficient
9)Explain the law for powers with an exponent of zero:The exponent law for powers with an exponent of zero is any power with an exponent of zero equals one (except zero).
10)Use patterns to show that a power with an exponent of zero is equal to one: 25= 32, 24=16, 23=8, 22=4, 21=2, 20=1
11)Explain the law for powers with negative exponents: First you have to reciprocal the base (9-2= ) and then you make the exponent positive (.
12)Use patterns to explain the negative exponent law:reciprocal the base and then to find the next one you multiply the denominator by 2. 2-1 = 2-2 = 2-3 = 2-4 =
13)I can apply the exponent laws to powers with both intergral and variable bases: Product law: 32x33 = 32+3 = 35 Quotient law: 5453=54-3=51 x4x3=x4-3=x1 Power law: (64)5 = 64x5=620 (x4)5= x4x5=x20 Zero law: 4545=45-5=40=1 x5x5=x5-5 = x0
14)I can identify the error in a simplification of an expression involving powers: 53x5254
Line 1. 53x2-4
Line 2. 56-4
Line 3. 52
Line 4. 25 The error is in line 1. It should be 53+2-4 not 53x2-4.
15)Use the order of operations on an expression with powers: to do an expression like this, you use BEDMAS, which means you start with brackets, then move to exponents, then division or multiplication in order they appear (left to right) and finally addition and subtraction in the order they appear (left to right). = 43+2+(3-1) = 47 = 16384
16)Determine the sum and difference of two powers: there is no law for this so you simply use BEDMAS. + = 36 + 216 = 252 - = 625 – 125 = 500
17)Identify the error in applying the order of operations in an incorrect solution: 42 + 45(48 x 43)
16+1024 (48x43)
1040 (65536 x 64)
1040 4194304
0.0002479553 The error in this expression is that they didn’t start in the brackets and then go to division, they did addition first.
18)Use powers to solve problems (measurement problems): If a package with a side length of 5 inches and there is a box of chocolates with a side length if 4 inches inside the package, how much free room is left in the package? 53 – 43 = 125 - 64= 61cm3
19)Use powers to solve problems (growth problems): If a sunflower is 2cm in height right now and it triples its height every day, how tall will it be in a week? 27 = 128 cm in height after one week,
20)Applying the order of operations on expressions with powers involving negative exponents and variable bases:
2-3+5
22-2
20 = 1 =