Question

For what value of x, the value of the expression becomes equal to 1 ?
${(2^{100}\times {2000}^{100})}^x=1$

• A. 1
• B. -1
• C. 0
• D. 100

Answer 1

The correct option is C 0

The expression is
${(2^{100}\times {2000}^{100})}^x$

You know, $a^x\times b^x={(a\times b)}^x=a{b}^x$
where a = 2 and b = 2000.

So,
${(2^{100}\times {2000}^{100})}^x=\{{(2\times 2000)}^{100}{\}}^x={\left({4000}^{100}\right)}^x={4000}^{100\times x}={4000}^{100x}$

Right hand side is equal to 1.

You know, $c^0=1whenc\ne 0$

Here, c = 4000.

$\therefore 100x=0$
$or,x=0$

So, the value of x = 0