AMC12 2000 A

AMC12 2000 A · Q2

AMC12 2000 A · Q2. It mainly tests Manipulating equations.

$2000(2000^{2000}) = x$ Find x.

$2000(2000^{2000}) = x$ 求 $x$。

(A) 2000^{2001} 2000^{2001}

(B) 4000^{2000} 4000^{2000}

(D) 4,000,000^{2000} 4,000,000^{2000}

(E) 2000^{4,000,000} 2000^{4,000,000}

Answer

Correct choice: (A)

正确答案：（A）

Solution

We can use an elementary exponents rule to solve our problem. We know that $a^b\cdot a^c = a^{b+c}$. Hence, $2000(2000^{2000}) = (2000^{1})(2000^{2000}) = 2000^{2000+1} = 2000^{2001} \Rightarrow \boxed{\textbf{(A) } 2000^{2001}}$. Solution edited by armang32324 and integralarefun

我们可以使用一个基本的指数运算规则来解决。我们知道 $a^b\cdot a^c = a^{b+c}$。因此， $2000(2000^{2000}) = (2000^{1})(2000^{2000}) = 2000^{2000+1} = 2000^{2001} \Rightarrow \boxed{\textbf{(A) } 2000^{2001}}$. Solution edited by armang32324 and integralarefun

Topics

AL.016 Manipulating equations