Exponents Multimedia Project
Exponents rules:
Zero Power Rule:
Whenever a number or variable is put to the power of zero the solution is 1
Ex:
3⁰ = 1
x⁰ = 1
(345xy)⁰ = 1
Product Rule:
When two variables are multiplied, their exponents will be added together
Ex:
x² ⋅ x³ = x⁵
x⁵y³ ⋅ x⁴y⁴ = x⁹y⁷
Quotient Rule:
The quotient rule is when you have variables within a fraction, their exponents are subtracted from each other
Ex
x
--- = 1
x
x⁷
--- = x⁴
x³
Power of a Power Rule:
When you have a variable within parenthesis with an exponent on the outside of the parenthesis, you multiply the two exponents together
Ex:
(x⁴)⁴ = x¹⁶
(y)² = y²
Distributive Power Rule:
The distributive power rule is essentially the same as the power of a power rule, but it's with more than one variable
Ex:
(x⁶y⁷)² = x¹²y¹⁴
Negative Exponent Rule
When you have a negative exponent, what you should do is flip the variable/number with the exponent from the numerator to the denominator, or if it's in the denominator, it goes from the denominator to the numerator.
Ex:
1
x⁻³ = ---
x³
x⁷
x⁷y⁻⁹ = ---
y⁹
Whenever a number or variable is put to the power of zero the solution is 1
Ex:
3⁰ = 1
x⁰ = 1
(345xy)⁰ = 1
Product Rule:
When two variables are multiplied, their exponents will be added together
Ex:
x² ⋅ x³ = x⁵
x⁵y³ ⋅ x⁴y⁴ = x⁹y⁷
Quotient Rule:
The quotient rule is when you have variables within a fraction, their exponents are subtracted from each other
Ex
x
--- = 1
x
x⁷
--- = x⁴
x³
Power of a Power Rule:
When you have a variable within parenthesis with an exponent on the outside of the parenthesis, you multiply the two exponents together
Ex:
(x⁴)⁴ = x¹⁶
(y)² = y²
Distributive Power Rule:
The distributive power rule is essentially the same as the power of a power rule, but it's with more than one variable
Ex:
(x⁶y⁷)² = x¹²y¹⁴
Negative Exponent Rule
When you have a negative exponent, what you should do is flip the variable/number with the exponent from the numerator to the denominator, or if it's in the denominator, it goes from the denominator to the numerator.
Ex:
1
x⁻³ = ---
x³
x⁷
x⁷y⁻⁹ = ---
y⁹
Multimedia project question:
For the Exponents Multimedia project, I have come up with the problem of:
(16x⁴y⁹)(4x¹ ⁄ ⁴y²)
-----------------------
32xy⁻²
Now to solve this problem, first we have to multiply the numerator together.
16 ⋅ 4
x⁴ ⋅ x¹ ⁄ ⁴
y⁹ ⋅ y²
The first equation is the most simple, all you have to do is multiply.
16 ⋅ 4 = 64
The second equation and the third are both solved the same way, you add the exponents.
x⁴ ⋅ x¹ ⁄ ⁴ = x ¹⁷ ⁄ ⁴
y⁹ ⋅ y² = y¹¹
Now that the numerator has been simplified, lets simplify the denominator.
For the 32, all you have to do is have the other whole number on the top be divided by it.
16 divided by 32 = 2
2 will now replace 32.
Now to get the new numerator, simply reverse the equation.
32 divided by 16 = 1
16 is replaced with 1.
Now for the x, we have to subtract the denominator x from the numerator x to get the new number
x ¹⁷ ⁄ ⁴ divided by x = x¹³ ⁄ ⁴
Finally we have to switch the denominator y to the numerator because it has a negative exponent, but since there's another y up there we have to add them
y¹¹ + y² = y¹ ³
And finally we are left with the answer of:
1x¹⁷ ⁄ ⁴y¹ ³
-------------
2
(16x⁴y⁹)(4x¹ ⁄ ⁴y²)
-----------------------
32xy⁻²
Now to solve this problem, first we have to multiply the numerator together.
16 ⋅ 4
x⁴ ⋅ x¹ ⁄ ⁴
y⁹ ⋅ y²
The first equation is the most simple, all you have to do is multiply.
16 ⋅ 4 = 64
The second equation and the third are both solved the same way, you add the exponents.
x⁴ ⋅ x¹ ⁄ ⁴ = x ¹⁷ ⁄ ⁴
y⁹ ⋅ y² = y¹¹
Now that the numerator has been simplified, lets simplify the denominator.
For the 32, all you have to do is have the other whole number on the top be divided by it.
16 divided by 32 = 2
2 will now replace 32.
Now to get the new numerator, simply reverse the equation.
32 divided by 16 = 1
16 is replaced with 1.
Now for the x, we have to subtract the denominator x from the numerator x to get the new number
x ¹⁷ ⁄ ⁴ divided by x = x¹³ ⁄ ⁴
Finally we have to switch the denominator y to the numerator because it has a negative exponent, but since there's another y up there we have to add them
y¹¹ + y² = y¹ ³
And finally we are left with the answer of:
1x¹⁷ ⁄ ⁴y¹ ³
-------------
2
Reflection Questions
itQuestion 1:
"What did I learn? What might I have learned, practiced, or improved my understanding of that may not be obvious? What was most interesting? Least? How can I learn new things if I’m not ‘interested in’ what I’m learning? What do others do in these cases to learn? What was clear, confusing, and somewhere in the middle? What do I still ‘need help’ with?"
Answer:
Well, I think the main thing that I've learned is that I'm not allowed to write fractions normally. Secondly I relearned the old exponent rules. And lastly I learned that the class has a wide range of difficulty for any one subject.
Question 2:
"What should I do with what I learned and know? What will I be able to do with this–both now and if and when I improve my understanding of it? Who should I ‘tell’ or share this with? Who would care and/or benefit the most?"
Answer:
Well, what I should do with what I've learned is use it to do better in class.
"What did I learn? What might I have learned, practiced, or improved my understanding of that may not be obvious? What was most interesting? Least? How can I learn new things if I’m not ‘interested in’ what I’m learning? What do others do in these cases to learn? What was clear, confusing, and somewhere in the middle? What do I still ‘need help’ with?"
Answer:
Well, I think the main thing that I've learned is that I'm not allowed to write fractions normally. Secondly I relearned the old exponent rules. And lastly I learned that the class has a wide range of difficulty for any one subject.
Question 2:
"What should I do with what I learned and know? What will I be able to do with this–both now and if and when I improve my understanding of it? Who should I ‘tell’ or share this with? Who would care and/or benefit the most?"
Answer:
Well, what I should do with what I've learned is use it to do better in class.
Citations
https://www.i2symbol.com/symbols/superscript
https://www.cuemath.com/algebra/exponent-rules/
https://www.cuemath.com/algebra/exponent-rules/