I'm also a fan of yours... I'm also "old", but I was a math major oh so many years ago. Your presentation are a great review in helping me recover the skills I once had.
Greetings. The answer is 2 raised to the 8 power. The value is determined as follows, 2^3 ÷ 2 ^ -5 is the same as 2^3 ÷ by 1 upon 2^5 which is the same thing as 2^3 × 2^5/1 after the inversion. Now we have 2 raised to the power of (3 + 5) = 2^ 8.
My thought is that if he is encouraging the non-use of calculators when not necessary, then it seems less optimal for someone to figure out by hand a number that involves a lot of multiplying by hand, i.e. raising it to the 8th power.
He actually does explain and use this rule. At 6:43 he goes over this rule, then he applies it to this problem at about 8:42 (after asking us to subscribe, yada yada). He then recaps it: When there is division of the powers*, you subtract the exponent* in the denominator from the exponent in the numerator.
real simple we have a division sign and a negative exponent on the constant to the right of the division sign. This means we "ignore" the negative exponent rule, rewrite the problem as a multiplication problem but because of the "ignore" part I mentioned we do NOT flip it. (ordinarily if the problem was written as a multiplication problem or if the exponent was NOT negative we would take the reciprocal of it) So this problem is actually (2^3) * (2^5) (2^3) * (2^5) is (2 * 2 * 2) * (2 * 2 * 2 * 2 * 2) which is 8 * 32. Which of course is 256. edited for spelling
super simple. PEMA says multiplication is just division raised to the -1 power. (Example 4 divided by 5 is the same as saying 4 * [ 5 ^ -1 ] ) We have division AND a negative exponent attached to the number so we don't flip, make the negative 5 just 5 and replace the division symbol with multiplication. this gives us 2 cubed and 2 raised to the fifth power. We can add exponents so we get 2 to the 8th or 256.
Another basic rule that I have somehow forgot after 50 years! It’s fun relearning how to solve these problems. Healthier than listening to politics, for sure!
One critique. You CAN move 1/ y^5 into y ^ -5. HOWEVER, you even stated the rule in this video that negative exponents are NOT fully simplified. Therefore, you should not do this and think your answer is correct.
I think the answer is 2 to the -2 or .02. I am not sure though. I see my mistake. I subtracted the exponents. However, I neglected the (-). I subtracted 3-5 and it should have been 3-(-5) which would have made the 5 positive... thus making the answer 2 to the 8th power. A simple thing as missing the right sign can cause you to get a simple problem wrong.
But you counted 3-(-5) was wrong, isn't it!!?? Answer should be -2. How come we can conclude 3+5 as answer 8... If we do totally opposite instead of - minus we do plus + then is only possible answer will be 8
How can they get confused. When you do ide like bases write down the base and subtract the exponents. So it's 2^8. maybe you are confused. And also give me the name of the tablet you are using so that I can as confused as you. Thanks
Glancing through the comments, it seems a lot of people, before watching the video I assume, got the result 2^−2 aka 0.25, and sometimes the negative of that, which suggests that one major source of confusion is in how to subtract a negative and another is in the proper treatment of negative exponents.
"You don't want to do too many steps in your brain". Why not just teach the simple multiplicative pattern that is repeated multiplication and its inverse repeated division, a.k.a. exponents? This is everything wrong with math instruction...instead of teaching the simple underlying pattern, the instructor veils this simple pattern with algebraic equivalent expressions and explains how to solve these using memorized steps...yuck!
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I'm a fan of yours.....I'm 70 years old and struggled with Algebra all my life.....
I'm also a fan of yours... I'm also "old", but I was a math major oh so many years ago. Your presentation are a great review in helping me recover the skills I once had.
Greetings. The answer is 2 raised to the 8 power. The value is determined as follows, 2^3 ÷ 2 ^ -5 is the same as 2^3 ÷ by 1 upon 2^5 which is the same thing as 2^3 × 2^5/1 after the inversion. Now we have 2 raised to the power of (3 + 5) = 2^ 8.
For anyone who works with binary systems they would recognize that 2 exp 8 is 256. Isn't it proper to clear the exponent in the answer?
My thought is that if he is encouraging the non-use of calculators when not necessary, then it seems less optimal for someone to figure out by hand a number that involves a lot of multiplying by hand, i.e. raising it to the 8th power.
theres one more rule. learnt it in some books. when exponents are divided like this the powers are subtracted so 3-(-5) equals 3+5 so easy 8
Yes, it was weird for me that he didn’t use that
He actually does explain and use this rule. At 6:43 he goes over this rule, then he applies it to this problem at about 8:42 (after asking us to subscribe, yada yada). He then recaps it: When there is division of the powers*, you subtract the exponent* in the denominator from the exponent in the numerator.
real simple we have a division sign and a negative exponent on the constant to the right of the division sign. This means we "ignore" the negative exponent rule, rewrite the problem as a multiplication problem but because of the "ignore" part I mentioned we do NOT flip it. (ordinarily if the problem was written as a multiplication problem or if the exponent was NOT negative we would take the reciprocal of it) So this problem is actually (2^3) * (2^5)
(2^3) * (2^5) is (2 * 2 * 2) * (2 * 2 * 2 * 2 * 2) which is 8 * 32. Which of course is 256.
edited for spelling
Thank you for breaking this down. You made it really clear.
2x2x2x1x1 in the numerator. Match the number of numerals you’ll have in the denominator with as many x1s as necessary.
Out of curiosity: how come the sign in front of the base doesn't change when switching the powers from numerator to denominator or vice versa?
super simple. PEMA says multiplication is just division raised to the -1 power. (Example 4 divided by 5 is the same as saying 4 * [ 5 ^ -1 ] )
We have division AND a negative exponent attached to the number so we don't flip, make the negative 5 just 5 and replace the division symbol with multiplication. this gives us 2 cubed and 2 raised to the fifth power. We can add exponents so we get 2 to the 8th or 256.
What i know before i look into vid is 2³ ÷ 2-⁵ = 8 ÷ 1/2⁵ = 8 × 32/1 = 256
Good Math just a hard way to do it. Easier: 2^3 ÷ 2^-5 => 2^3 x 2^5 => 2^8 = 256
And you are exactly right. Congrats.
Negative exponents are used all the time in science. Where do you get this stuff?
Another basic rule that I have somehow forgot after 50 years! It’s fun relearning how to solve these problems. Healthier than listening to politics, for sure!
One critique. You CAN move 1/ y^5 into y ^ -5. HOWEVER, you even stated the rule in this video that negative exponents are NOT fully simplified. Therefore, you should not do this and think your answer is correct.
256 in three seconds. Good video.
You subtract -5 from 3. 3 - (-5) = 8 2 to the 8th power = 256
I think the answer is 2 to the -2 or .02. I am not sure though. I see my mistake. I subtracted the exponents. However, I neglected the (-). I subtracted 3-5 and it should have been 3-(-5) which would have made the 5 positive... thus making the answer 2 to the 8th power. A simple thing as missing the right sign can cause you to get a simple problem wrong.
But you counted 3-(-5) was wrong, isn't it!!?? Answer should be -2.
How come we can conclude 3+5 as answer 8... If we do totally opposite instead of - minus we do plus + then is only possible answer will be 8
huh?
Normally you want answers "simplified" so shouldn't take that 2 to the 8th power to SIMPLY 256?
I'm a little rusty about -negative numbers. But the first numbers = 6. The total, I'm not sure.
2³=
2×2×2=
8
not 6
🤦♂️
It happens lol.
Elizabeth if you are a bit rusty try vinegar. It removes rust and tablet class maths
Thanks
You got me. I apprached it the proper way and got 2^8 = 256 I do all my Mats on pen and paper
I'd buy every class you have that i would need but your prices are too high.
512, I went x2 TOO MANY but I knew 2 to the 8th power.😮😊
never enjoyed math like I do now 👍
thank you very very^10 much*
I calculated out the actual numerical value 256.
When you know the rules of power it's not that difficult.
2³ : 2^-5 = 2^[3-(-5)] = 2^(3+5) = 2^8 = 256
The answer is 2 to the eighth power or 256. I like your first solution the best because you don't have to invert.
Is 2^8 or 256
You failed to complete the problem! The correct answer is 256.
Which is the same as 2^8!
2^8
I like your videos, but 3/5's of the time you talk, I am learning nothing! You take too long !
So long I just didn't finish listening
2 to the power of 8
yeah...confused. i have forgotten how. :(
2⁸ 0:14
2>8 maybe
2^8 = 256
2 power 8
1/4? I didn't know negative exponents were a thing.
2^8 in 10s
presentation issue here 3 - (-5) is 8 ....yep
How can they get confused. When you do ide like bases write down the base and subtract the exponents. So it's 2^8. maybe you are confused. And also give me the name of the tablet you are using so that I can as confused as you. Thanks
Glancing through the comments, it seems a lot of people, before watching the video I assume, got the result 2^−2 aka 0.25, and sometimes the negative of that, which suggests that one major source of confusion is in how to subtract a negative and another is in the proper treatment of negative exponents.
2 to the power 8
Ans 1/4
M'kay...🤟🏽
-8
3+5=8 is power of 2
4
256 is the answer
You waste too much time with frivolous ramblings. Get to the point.
1/4
You are why people hate math? Talk about complicating something simple??
-.25
Eight
I meant two to the eighth not just eight.
256
Ok 2 power 8 is the same thing
One sec question 😂
easy
Ok I’m lost😢
-.6
-1/4
1/4. Crap, I screwed it up; I was doing it in my head. Should have used a crayon and paper!
- 1/8
You talk too much. I become exhausted and become confused.
I agree. Too much talking
it .44444and it carry ion from julius wilson dixmoor ill lifehouse aug 31 2023 18:51
"You don't want to do too many steps in your brain". Why not just teach the simple multiplicative pattern that is repeated multiplication and its inverse repeated division, a.k.a. exponents? This is everything wrong with math instruction...instead of teaching the simple underlying pattern, the instructor veils this simple pattern with algebraic equivalent expressions and explains how to solve these using memorized steps...yuck!
Your word “multiplicative” hurt my brain!
What do you even mean? I can’t decipher what you’re suggesting.
You talk to much!
Lost me
2^8
-8
256
-1/8
2^8
256
2^8
256
4^8
256
2^8
256