Take 1/4 to the 3/2 power without using a calculator - what is the answer? Algebra Powers Rules

[@jald910]

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

[@tomtke7351]

(1/4)^(3/2) = ((1/4)^(1/2))^3 =(sqrt(1/4))^3 =(1/2)^3 =(1/8)

[@thomasharding1838]

1/4 cubed = 1/64 and the square root of that is 1/8. Thank you for the refresher!

[@robpatterson2861]

I love the way you teach!

[@panlomito]

1/4 = 2 ^ -2 so 2 ^ (-2 . 3/2) = 2 ^ -3 = 1 / (2 . 2 . 2) = 1/8 Nice !

[@Stylux-z1p]

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✔

[@Shay-q8u]

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)

[@chrisdissanayake6979]

Answer: 1/8 ------------ (1/4)^3/2 (1/2^2)^3/2 1 -- 2^3 1/8

[@mylittlepitbull3143]

In my head. No pencil. 1/8, I still got the magic touch. Basically, the square root of 1/4, cubed.

[@terry_willis]

Yes, I found it easier to just take the sq.rt of (1/4)^3. John's way was more complex and longer.

[@DavidRobinson-rj2sp]

@@terry_willis: Yep, that's the method I used too.

[@DavidRobinson-rj2sp]

I did square root of 1/4 = 1/2 then 1/2 cubed = 1/8.

[@russelllomando8460]

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

[@fron3107]

Isn't it funny how some videos just disappear over night?

[@mauriziograndi1750]

No calculator ok, then 1/4^3 is 1/64 (4^3=64) Sqrt of 1/64 is 1/8.

[@Sellout-Singh]

1/6

[@CawasKapadia]

1/8

[@CobraQuotes1]

69?

[@stevendebettencourt7651]

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?

[@cheriem432]

I really wish you would not go over more basic math before you solve every problem.

[@danielmorehouse9116]

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?

[@josephlaura7387]

1/8

[@artgilkey1547]

1/8

[@charlesmitchell5841]

1/8