Indices

Algebra Level 1

2000 ( 2000 2000 ) = ? \large \color{#D61F06}{2000}\left(\color{#3D99F6}{2000}^{\color{#20A900}{2000}}\right) = \, \color{#69047E}?

200 0 2001 2000^{2001} 200 0 4000 2000^{4000} 400000 0 2000 4000000^{2000} 400 0 2000 4000^{2000} 200 0 4000000 2000^{4000000}

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16 solutions

Danish Ahmed
Mar 25, 2015

2000 ( 200 0 2000 ) = ( 200 0 1 ) ( 200 0 2000 ) = 200 0 2001 2000(2000^{2000}) = (2000^{1})(2000^{2000}) = 2000^{2001}

Harsh Kumar
Mar 29, 2015

Ha..a simple one indeed..its the 3rd law of indices that if x a ( x b ) x^{a} ( x^{b}) , then it will be x a + b x^{a+b} , hence in this 200 0 1 + 2000 2000^{1+2000} = 200 0 2001 2000^{2001}

If I could down vote you for arrogance I would.

John Walenczyk - 2 years, 7 months ago
Ramez Hindi
Apr 1, 2015

a × ( a a ) = a 1 × a a = a a + 1 a\times({a}^{a})={a}^{1}\times{a}^{a}={a}^{a+1} where a Z a \in \mathbf{Z}

Put a = 2000 a=2000 so you will get the desire result

8ⁿ is a decimal. So. It's 2000²ⁿⁿ¹

Am Kemplin - 3 weeks, 3 days ago

200 0 1 × 200 0 2000 = 200 0 1 + 2000 = 200 0 2001 2000^1 \times 2000^{2000}=2000^{1+2000}=\boxed{\large{2000^{2001}}}

2000 ( 200 0 2000 ) 2000(2000^{2000}) = 200 0 1 + 2000 = 2000^{1 + 2000} = 200 0 2001 = 2000^{2001}

Aaron Ma
Oct 20, 2020

We can just use the Product Rule for this problem:

2000 ( 200 0 2000 ) = 200 0 2000 + 1 = 200 0 2001 2000(2000^{2000}) = 2000^{2000 + 1} = 2000^{2001}

2000(2000 2000 )=(2000 1 )(2000 2000 )=2000 2001

laws of exponents

Adarsh Mahor
Dec 11, 2015

This most easy problem but just 65% people have solved this problem
!!!!!!!!!!!!!!!! Amazing!!!!!!!!!!!!!!!!!

Jaswinder Singh
Jul 6, 2015

Base same and power add

Purnima Sharma
Jun 3, 2015

2000(2000^2000)=(2000^1)(2000^2000) =2000^1+2000 =2000^2001

Katia García
May 23, 2015

Lets see how many times we are multiplying 2000, there are 2000times so that is multiplied by one more 2000, there for it's 2001 times being multiplied. The answer is 2000²°°¹

2000(2000^2000) = 2000 x 2000^2000 = 2000^2001

(X^m)(X^n)=X^m+n

2000^1(2000^2000)=2000^2000+1

Hans Varona
Apr 4, 2015

let 2000 = x; x^1*x^2000=x^2001

im not sure

Frex Cuadillera
Apr 3, 2015

2000(2000^2000)= 2000^1(2000^2000) =2000^2000+1 = 2000^2001 this is one of the law of exponents

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