Download Everything I know about exponents

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
1
1
1
(9-2= 9−2 ) and then you make the exponent positive (9−2 = 92 ).
12) Use patterns to explain the negative exponent law: reciprocal the base and then to find
1
1
1
1
the next one you multiply the denominator by 2. 2-1 = 2 2-2 = 4 2-3 = 8 2-4 = 16
13) I can apply the exponent laws to powers with both intergral and variable bases:
Product law: 32x33 = 32+3 = 35 𝑥 2 × 𝑥 3 = 𝑥 2+3 = 𝑥 5 Quotient law: 54÷53=54-3=51 x4÷ x3=x4-3=x1
Power law: (64)5 = 64x5=620 (x4)5= x4x5=x20 Zero law: 45÷45=45-5=40=1 x5÷x5=x5-5 = x0
14) I can identify the error in a simplification of an expression involving powers:
53x52÷54
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 × 42 + (43 ÷ 41 ) = 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. 62 + 63 = 36 + 216 = 252 54 - 53 = 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 × 25 ÷ 22
𝑥 5 × 𝑥 −6 ÷ 𝑥 7
2-3+5
22-2
20 = 1
𝑥 5+−6
𝑥 −1−7
1
𝑥 −6 = 𝑥 6