Take 1/4 to the 3/2 power without using a calculator - what is the answer? Algebra Powers Rules
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- เผยแพร่เมื่อ 8 ก.พ. 2025
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Wow... like your worked out solution; what a refresher.
My way:
(1/4)^(3/2) = sqrt(1/4^3) = sqrt(1/4*4*4) = sqrt(1/64) = 1/8
I love the way you teach!
Very pleased with myself, in head without having to think, which makes a nice change.
Got 1/8. Hooray I remember how to do this even though I’ve never needed to do such a problem in real life since the last math class I took 50 plus years ago
(1/4)^(3/2)
= ((1/4)^(1/2))^3
=(sqrt(1/4))^3
=(1/2)^3
=(1/8)
1/4 cubed = 1/64 and the square root of that is 1/8. Thank you for the refresher!
I did square root of 1/4 = 1/2 then 1/2 cubed = 1/8.
super simple I believe my country teaches this in the 6th grade.
we have a fraction for an exponent this means the numerator is a power and the denominator is the root
I have a 4 which is 2² I multiply in the numerator of the exponent to get 2 raised to the 6th power which is 64.
This makes the question (1/64) ^ 1/2 so the answer is 1/8
(I teach grades 8 through 12 and this is expected knowledge before entering my normal level math course)
4 = 2² , 1/p² = p^-2 , (s²)³ = s² * ³ = s^6
--------------------------------
[1/4]^3/2 = [1/2²]^3/2
[2^-2]^3/2 = [2]^(-2 * 3/2)
[2]^(-2 * 3/2) = [2^-3] = 1/ 2³ = 1/8✔
1/4 = 2 ^ -2 so 2 ^ (-2 . 3/2) = 2 ^ -3 = 1 / (2 . 2 . 2) = 1/8 Nice !
Answer: 1/8
------------
(1/4)^3/2
(1/2^2)^3/2
1
--
2^3
1/8
I did this in less than 20:seconds. I wish I could remember the process In was taught and used.
=1/8
No calculator ok, then 1/4^3 is 1/64 (4^3=64)
Sqrt of 1/64 is 1/8.
In my head. No pencil. 1/8, I still got the magic touch.
Basically, the square root of 1/4, cubed.
Yes, I found it easier to just take the sq.rt of (1/4)^3. John's way was more complex and longer.
@@terry_willis: Yep, that's the method I used too.
Isn't it funny how some videos just disappear over night?
woo hoo got 1/8 it's sr of (1/4)^3 numerator is the power & denominator is the root
(1/4)^3 = 1/64 sr of (1/64) = 1/8 thanks fopr the fun
sqrt(1/4^3) Nuff said. This channel is a complete waste of time. SAYONARA
1/8
This is a pretty cool one. Let’s dig in.
(1/4)^(3/2)
Cool Fact: (a/b)^c = (a^c)/(b^c). Therefore:
= (1^(3/2))/(4^(3/2))
For the numerator, we know that 1^x = 1 for any real number x:
= 1/(4^(3/2))
Cool Fact: a^(b/c) = (a^b)^(1/c) = (a^(1/c))^b. We’re gonna go with the last equation:
= 1/((4^(1/2))^3)
Cool Fact: x^(1/2) = sqrt(x). Therefore:
= 1/((sqrt(4))^3)
= 1/(2^3)
= 1/8
And that’s the answer. Questions?
1/6
I really wish you would not go over more basic math before you solve every problem.
1초도 안걸릴 간단한 문제를 어렵게 설명하네
1/4 은 1/2 의 재곱이니 문제의 답은 당연히 1/2의 3재곱인걸로 바로 답이 나오는데....
69?
This is Zimmerman, NOT AndyMath!
2 to the 3rd power is the same as multiplying two by itself 3 times? You're using 2 as factor 3 times but you only multiply 2 by itself TWO times. 2x2x2. How many multiplication signs do you see?
1/8
1/8
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