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Algebra Level 1

5 55 + 5 55 + 5 55 + 5 55 + 5 55 = ? \large \color{#624F41}5^{55} + \color{#624F41}5^{55} + \color{#624F41}5^{55} + \color{#624F41}5^{55} +\color{#624F41} 5^{55} = \, ?

5 56 5^{56} 5 275 5^{275} 2 5 56 25^{56} 2 5 275 25^{275}

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27 solutions

Parth Lohomi
Jan 18, 2015

Because a + a + + a n number of a ’s = a × n \Large\underbrace{a+a+ \ldots+a}_{n \text{ number of }a\text{'s}} = a\times n , we have

5 55 + 5 55 + 5 55 + 5 55 + 5 55 = 5 55 × 5 = 5 55 × 5 1 5^{55} + 5^{55} + 5^{55} + 5^{55} + 5^{55} = 5^{55} \times 5 = 5^{55} \times 5^1

By the Rules of Exponents , we get 5 55 × 5 1 = 5 55 + 1 = 5 56 5^{55} \times 5^1 = 5^{55 + 1} = 5^{56} .

So the answer is 56.

I can understand this but I dont agree with this solution!!!

Ben Hunter - 5 years, 4 months ago

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Just simply think, 5^55 + 5^55 + 5^55 + 5^55 + 5^55 = 5^55 (1 + 1 + 1 + 1 + 1) = 5 x 5^55 = 5^56.

A Former Brilliant Member - 3 years, 3 months ago

I also didn't understand at first but now I do. So what you should do first is, factorise the sum. Then you solve it. Hope it helps.

The Guy - 5 years ago

Trying to understand this behavior better. What would the solution be if the question asked: 5^{55}+5^55+5^55+5^55=

Thank you!

Brion Hickey - 5 years, 3 months ago

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Remember that repeated addition is just multiplication. Since this is repeated four times, the answer would be 4 × 5 55 4 \times 5^{55} .

Zain Majumder - 2 years, 9 months ago

Where is the 5^1 comming from??

Elizabeth Magelky - 5 years, 1 month ago

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exactly Elizabeth

Ben Hunter - 5 years ago

5^55 + 5^55 + 5^55 + 5^55 + 5^55

5^55 x 5

••••••••• 5 = 5^1

so...

5^55 x 5^1

Gabrielle Caram - 5 years, 1 month ago

That is the variable 'n'

There are 5 units of 5^55. So 'n' is 5 or can also be written as 5^1

Anway Pramanik - 4 years, 11 months ago

Factor 5^55 you get 5^55 x (1+1+1+1+1) which is equal to 5^55 x 5 which is the same as saying 5^55 x 5^1 which is 5^56 by definition

Khalid Jomha - 5 years, 1 month ago

Of course, it is 5 to the 56th power. I am quite rusty with algebra. I used to teach it when the math teacher was absent. But, that was ten years ago. This is a great site. I hope to hone my skills over time. Thanks much.

Joe Tully - 5 years ago

awosome way.....

Saddam Adnan - 5 years, 3 months ago

Look this situation..

2²+2²+2² =

(Obvius is 12 but) But, in the resolution you given us.. 2² because repeat 2³ because number of 2

2² . 2³ = 2^5

It is 32 ... This results don't make sense. Sorry party lohomi it is wrong.

kauan horvath - 5 years, 2 months ago

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It is 2^2(1+1+1) or 4(3)=12 . The solution is right

Sai Venkatesh - 5 years, 2 months ago

You did it wrong mate

Shadman I - 5 years, 2 months ago

In their explanation it was 5^55 x 5^1. Since both had a base of 5 her solution works. Yours is 2^3 x 3^1. The bases are different. Exponent rules only apply to same base 5 and 5. Not 2 and 3. Hope this helps!

David Parsons - 5 years, 2 months ago

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thanks! You saved me

Gabrielle Caram - 5 years, 1 month ago

According to this solution, 2^2+2^2+2^2=2^2*3^1

emmanuel daniel - 5 years ago

No! It becomes 2^2*2^1=2^(2+1)=2^3

Anway Pramanik - 4 years, 11 months ago

5^55*5^1=5^56

Mathiyazhagi Malligabanu - 5 years, 1 month ago

Wrong and wrong

albert afiembo - 5 years, 1 month ago

I think it is not possible for all problems

Prince Shanmuka - 5 years ago

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Yep but it was possible for this So,we used it

candy blocs - 12 months ago

I'm sorry but 5^56 is not the correct answer to this question. 5^56 = (5^55) + 5×5. The correct answer to the question is not (5^55) + 5×5. Misinforming people is not a good thing to do.

Sunny Sidhu - 4 years, 3 months ago

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You have no clue whqt you are talking about. Your incorrect answer woule be 5^57

A Former Brilliant Member - 3 years, 6 months ago

It will be helpful if you can explain in more detail. Thanks

Archita Anand - 2 years, 10 months ago

why does my calculator say the answer is 2.5^56? weird

Doug Forbes - 2 years, 3 months ago

This is all shit

barcsandsal Barclay - 1 year, 10 months ago

How did you get this solution? Your explanation does not make sense.

Seth Stewart - 8 months, 2 weeks ago

I. Can't understand

olarewaju alabi - 3 months, 3 weeks ago

Wow I just remembered it now because we saw this the last year at school thank u

ooh_ AR - 3 months, 2 weeks ago

this is a piece of shit.

Am Kemplin - 1 month, 1 week ago

You would add all of the exponents to a total. an exponent of 56 is just one more than 55 therefore it does not answer the question. If it was 5 with an exponent of 55 + 5 with and exponent of 1 then the answer would be correct.

Taylor Desotell - 5 years, 2 months ago

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Increasing the exponent by one does not increase the value by one. In this case, it multiplies the value by 5.

Zain Majumder - 2 years, 9 months ago

a+a+a would be a to the 3rd

Taylor Desotell - 5 years, 2 months ago

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No, a+a+a =3a

Lin Clarkson - 5 years, 1 month ago

No, a X a X a = a^3

Anway Pramanik - 4 years, 11 months ago

5× (5^55) does not equal 5^56.

Sunny Sidhu - 4 years, 3 months ago

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You have to distribute the 5 to the exponent as well, which the guy who wrote the question failed to do.

Sunny Sidhu - 4 years, 3 months ago

Yes, it does. One law of exponents is that a n × a m = a n + m a^n \times a^m = a^{n+m} . So 5 1 × 5 55 = 5 1 + 55 = 5 56 5^1 \times 5^{55} = 5^{1+55} = 5^{56} .

Zain Majumder - 2 years, 9 months ago

I thought this: First, substitute 5 with x, and the expression becomes 5x^55. You do 5×5= 25^55

Matilde Mori - 4 years, 9 months ago

agreed! brilliant..

Muhammad Aimal Rehman - 5 years, 3 months ago
Bala Murugan V
Jan 22, 2015

the Solution is

Wow this helped so much

Austin Settje - 5 years, 2 months ago

Wow nice solution

Charan Singh - 5 years ago

Best solution sir

Prathamesh Patil - 4 years, 10 months ago

Easiest way.

Nida Fatima - 3 years, 6 months ago

This is correct.

Nikolas Кraj - 2 years, 7 months ago

This answer helped explained it better. Thank you.

Frank Duodu - 10 months, 2 weeks ago

Now this is helpful than abovd

Pulkit Sharma - 5 months ago

This is incorrect.

Sunny Sidhu - 4 years, 3 months ago
Syauqi Ramadhan
Jan 24, 2015

a + a = 2 ( a ) a+a = 2 (a)

5 55 + 5 55 + 5 55 + 5 55 + 5 55 = ( 5 ) 5 55 = 5 56 5^{55}+5^{55}+5^{55}+5^{55}+5^{55}=(5) 5^{55}= \boxed{5^{56}}

I like this solution.Logic.

Frankie Fook - 6 years, 3 months ago

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yes, it's logic and I can accept this.

Ellan Dandelion - 5 years, 6 months ago

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yes definitely easy to be understood :) :) ;)

Frankie Fook - 5 years, 6 months ago

Thank you. This one made it work for me

Chris Gilliom - 5 years, 4 months ago

Best example

Chris Gilliom - 5 years, 5 months ago

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yeah 100% indeed!

Frankie Fook - 5 years, 5 months ago

Write a comment or ask a question...like this

Sabina Bhuiyan - 5 years, 3 months ago

Finally this makes sense to me

Tony Lopes - 5 years ago

Why are we multiplying 5 by 5 and not 5 by the number that 5^55 equals to?

H F - 3 years, 6 months ago

This is why I’m hopeless with maths haha

Tim Lewis - 2 years, 4 months ago
Seán Vaeth
Aug 21, 2015

5 55 + 5 55 + 5 55 + 5 55 + 5 55 = 5 ( 5 55 ) 5^{55} + 5^{55} + 5^{55} + 5^{55} + 5^{55} = 5(5^{55}) = 5 1 5 55 = 5 1 + 55 = 5 56 = 5^{1} * 5^{55} = 5 ^{1 +55} = \boxed{5^{56}}

like explanation

Vasant Hadkar - 5 years, 4 months ago

You skipped 1 step (that would clarify your result)

Nick Popa - 10 months ago
Tytan Le Nguyen
Jan 18, 2015

You are just adding 5 55 5^{55} 5 times, meaning that it's just 5 56 5^{56} .

Write a comment or ask a question... This doesn't make sense. How can it only be to one more power if you just added it together five times?

Christian Brouillette - 6 years, 4 months ago

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Because adding the same thing 5 times or multiplying it by 5 is same.
And in this case multiplying by 5 will add one more power. Like, 5 × 5 2 = 5 × 5 × 5 = 5 3 5\times\boxed{5^{2}} =5\times5\times5 =\boxed{5^{3}}

MD Omur Faruque - 5 years, 11 months ago

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So what would the solution be if you only added four fives?

Wayne Proctor - 5 years, 5 months ago

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@Wayne Proctor That'll be just 4 × 5 55 4\times5^{55} . No simplification possible.

MD Omur Faruque - 5 years, 5 months ago

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@Md Omur Faruque So the answer to 5^55 added 4 times would be 20^55 but 5 just becaomes 5^56?

Tirzah Brown - 5 years, 4 months ago

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@Tirzah Brown The answer to 5^55 added 4 times would be 4x 5^55. You can not multiply the base (which is 5) four times to get the correct answer.

Ex: 2^2 + 2^2 + 2^2 = 3x2^2.....It would not be equal to 6x2^2 as your logic would say.

Rafael Toralba - 5 years, 3 months ago
Ankit Raj
Nov 20, 2015

Simply 5^55(1+1+1+1+1)

5^55(5)

5^(55+1)

5^56

OH ..................WHAT A NEW THING YOU HAVE DID

anshu garg - 4 years, 5 months ago

I downt no da answer too dis qussten

Am Kemplin - 1 month, 3 weeks ago
Krishna Chaitu
Nov 19, 2015

a^m×a^n=a^(m+n)

Ajin Varghese
Dec 24, 2015

=5^55 ( 1 + 1+1+1+1) =5^55 (5) =5^55 * 5^1 =5^(55+1) =5^56 = required solution .

Xi Guan
May 10, 2018

i use this method

5^1+5^1+5^1+5^1+5^1=5^2

5^2+5^2+5^2+5^2+5^2=5^3

5^3+5^3+5^3+5^3+5^3=5^4

5^4+5^4+5^4+5^4+5^4=5^5 . . .

5^n+5^n+5^n+5^n+5^n=5^n+1

so 5^55+5^55+5^55+5^55+5^55=5^55+1=5^56

Mohammad Khaza
May 17, 2017

5^55+5^55+5^55+5^55+5^55

=5*5^55

=5^1*5^55=5^56

very good explanation

Halima Tahmina - 4 years ago

thanks.your comment inspired me

Mohammad Khaza - 4 years ago

Just take 5^55 common from all terms. It becomes 5^55 (1+1+1+1)=5^55×5^1=5^56

555π ±333^2

Am Kemplin - 1 month, 3 weeks ago
Mahfuz Raihan
Jun 8, 2016

The Answer is write. In here, where is the problem?

5 55 + 5 55 + 5 55 + 5 55 + 5 55 5^{55} + 5^{55} +5^{55} +5^{55} +5^{55}

= 5 × 5 55 = 5 \times 5^{55}

= 5 1 × 5 55 = 5^1 \times 5^{55}

= 5 1 + 55 = 5^{1+55}

= 5 56 =5^{56}

Tom Wang
Jun 25, 2020

there are 5 5^55s which gives 5^56

Joshua Olayanju
May 20, 2020

It is a very simple problem 5^55 added by itself 5 times is equivalent to (5)5^55 which equals 5^56. I don't understand how only 53% of people got this right

Darsh Kedia
May 12, 2020

We know that a + a + + a n number of a ’s = a × n \Large\underbrace{a+a+ \ldots+a}_{n \text{ number of }a\text{'s}} = a\times n , so we have,

5 55 + 5 55 + 5 55 + 5 55 + 5 55 = 5 55 × 5 = 5 55 × 5 1 5^{55} + 5^{55} + 5^{55} + 5^{55} + 5^{55} = 5^{55} \times 5 = 5^{55} \times 5^1

By following Rules Of Exponents , we get 5 55 × 5 1 = 5 55 + 1 = 5 56 5^{55} \times 5^1 = 5^{55 + 1} = 5^{56}

So the answer is 5 56 5^{56} .

Marvin Kalngan
Apr 30, 2020

Laws of exponents.

Emily Peng
Nov 17, 2019

The above equation is equivalent to 5 × 5^55, or 5^56.

Jae Hyun Kim
Jan 16, 2019

If you are calaulating 2+2, 2+2=2 times 2= 2^2. Also, if you are calaulating 3^2+3^2+3^2=3(3^2)=3^3. On the same principle, 5^55+5^55+5^55+5^55+5^55=5(5^55)=5^56.

Tran Nguyen
Dec 30, 2018

We have 5 to the power of 55 added together 5 times, therefore it would be 5 times 5 to the power of 55, which would be 5 to the power of 56.

Gia Hoàng Phạm
Sep 19, 2018

5 55 + 5 55 + 5 55 + 5 55 + 5 55 = 5 55 ( 1 + 1 + 1 + 1 + 1 ) = 5 55 × 5 = 5 56 5^{55}+5^{55}+5^{55}+5^{55}+5^{55}=5^{55}(1+1+1+1+1)=5^{55} \times 5=\boxed{\large{5^{56}}}

Anshika Sinha
Feb 11, 2018

This Q. is based on a^m.b^n=a(^m+n) the Q. is 5^55+5^55+.....5^55=? and the ans is 5^55 ×5^1=5^55+1=5^56

Abhyuday Singh
Feb 4, 2017

5^55+5^55...5 times= 5^1*5^55=5^56

5^55+5^55+5^55+5^55+5^55 =5*5^55 =5^(1+55) =5^56

The answer is 5^56 because in the question 5^55 comes 5 times. So, we can simply do 5 * 5^55 and get 5^56 as the result.

Mark Barwood
Oct 24, 2016

Since this can be factorised to 5^55(1+1+1+1+1), which equals 5^55 multiplied by 5, by the laws of indecies it is equal to 5^56

Nwankpa Richard
Feb 10, 2016

5^55 (1+1+1+1+1) =5^55 (5) =5^56

In the equation 5^55 + 5^55 + 5^55 + 5^55 + 5^55, you can factor out a 5^55 from it, resulting in 5^55(1+1+1+1+1) = 5^55(1x5) = 5^55(5) = 5^55 x 5^1 = 5^(55+1) = 5^56

Nathanael Toms - 5 years, 1 month ago

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it's a so called drenanaton. But we have infinity and we need to put x in there. But if we did not have x in there then the math wouldint work. otherwise. it would be x=y which does not equal to anything.

Am Kemplin - 1 month, 3 weeks ago

death u Morons

Am Kemplin - 1 month, 3 weeks ago

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