Percentage Power

Algebra Level 2

$\Large {25\%}^{{50\%}}= \, ?$

12.5% 5% 50% 125%

7 solutions

Akhil Bansal
Dec 18, 2015

$\large \color{#20A900}{25 \%} = \dfrac{25}{100} = \dfrac{1}{4} \quad ; \quad \color{#3D99F6}{50 \%}= \dfrac{50}{100} = \dfrac{1}{2}$ $\large \color{#20A900}{25 \%}^{\color{#3D99F6}{50\%}} = \left(\dfrac{1}{4}\right)^{\frac{1}{2}} = \dfrac{1}{2}$ $\dfrac{1}{2} \times 100\% = 50\%$

Actually $\frac{1}{2}=50\%$ , not $\frac{1}{2} \times 100 = 50\%$

Trung Đặng Đoàn Đức - 5 years, 5 months ago

Or even, $\dfrac{1}{2} \times 100 \% = 50 \%$

Raj Magesh - 5 years, 5 months ago

100% does not equal 100. It equals 1.

patrick dougherty - 5 years, 5 months ago

I think they meant 1/2 x 100%

Jack Bishop - 5 years, 5 months ago

Sorry, but why does 1/4 to the 1/2 equal 1/2?

Edward Walters - 5 years, 5 months ago

Square root of 1/4 is 1/2

diwahar kc - 5 years, 5 months ago

I get that it's the square root, but why? Does it always just halve?

Edward Walters - 5 years, 5 months ago

@Edward Walters – When you have a number to the 1/2 power, it means you square root the number. In this case you have the square root of 1/4. This is the same as $\frac{\sqrt{1}} {\sqrt{4}}$ , which is 1/2

Bailey Wilson - 5 years, 5 months ago

@Bailey Wilson – Ah! The last line was all I needed, but thanks! That makes sense now.

Edward Walters - 5 years, 5 months ago

@Edward Walters – The square root of .25 is .5 because .5^2 = .5 X .5 = .25

Laura Stewart - 5 years, 5 months ago

How the heck does that make any sense?

Rohan Zener - 5 years, 2 months ago

Thanks Akhil. It helped.

Arya Lewis - 2 years, 2 months ago

like how is this helping I should be getting better BUT IM NOT THANKS TO THIS BAD EXPLINATION

Alkimare A - 2 years, 2 months ago

Fin Moorhouse
Dec 17, 2015

$25\%=\frac{25}{100}=0.25$ and $50\%=\frac{50}{100}=0.5$ . Therefore $25\%^{50\%}=0.25^{0.5}=\sqrt{0.25}=0.5=50\%$ .

One thing is not mentioned.Wheather 25 % and 50% ARE of same number or like successive discount.In that case all solutions will be wrong.Why it is being asked? OK.Let us imagine the number is 100,then it's 25% is 25 ,then while goung to calculate 50% - - doubt comes that which ill be the power of 25 ?25 to the power 50 or 25 to the power 12.5.

ASOKE KUMAR GHOSH - 5 years, 5 months ago

I'm afraid I'm not entirely sure what you mean. 50% is a clearly defined number, equal to 0.5 or $\frac{1}{2}$ . The % sign indicates that $x\%=\frac{x}{100}$ (not the percentage of something in particular in this case). I don't see any ambiguity.

Fin Moorhouse - 5 years, 5 months ago

Yeah I feel like this problem is not well stated and has no unique solution

Josh Siglos - 5 years, 5 months ago

I think you're right and there's no ambiguity. 50% of any value say x is half of x and 25% of that half is simply 1/8x which is 12.5. However I see ill structuring of the problem here. It implies that 50% is to be raised and not multiplied. Hence the answer is 1/2 or 50%.

Mian Aamir - 5 years, 5 months ago

Tahmid Hossain
Dec 22, 2015

Write a solution.25Per.=1by4,50per.=1by2then root1by4=1by2=50per.

Michael Fitzgerald
Nov 15, 2017

$\large \color{#20A900}{25\%}^{\color{#3D99F6}{50\%}}= \left(\dfrac{1}{4}\right)^{\color{#3D99F6}\dfrac{1}{2}} = \left(\left(\dfrac{1}{2}\right)^{2}\right)^{\color{#3D99F6}\dfrac{1}{2}}\color{#333333}=\dfrac{1}{2}=50\%$

Tanvir Hasan
Jan 27, 2016

25% = 1/4 and 50% = 1/2 so, {(1/2)^2}^(1/2) = 1/2 as we see, 10% = 10/100 = .1 So, 1/2 or 0.5 must be 50% 😊

Ajay Ajay
Dec 30, 2015

25/100=0.25,50/100=0.5,(0.25)^0.5=0.5,0.5*100=50

Johnny Hyman
Dec 27, 2015

I just converted 25% and 50% into decimals, causing the equation to look like this: 0.25^0.5 = ? The answer I got was 0.5, so then I just converted 0.5 back into percent, so the answer is 50%.

Percentage Power

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