Question

For which value of "x" in the following expression, the final value will be equal to 1?$({{1000}^{100})}^x=1$

• A. 0

Answer 1

The correct option is A 0
We know that $a^0=1$ when a≠1.

So, if we can make the ultimate index of 1000 eqaul to zero, the final value of the expression will be equal to 1 only.

∴ ${\left({1000}^{100}\right)}^x={\left(1000\right)}^0$

We know ${\left(a^x\right)}^y=a^{x\times y}=a^{xy}$

So,
${\left({1000}^{100}\right)}^x={\left(1000\right)}^{100\times x}={\left(1000\right)}^{100x}$

You can get the final value as 1 when
$100\times x=0or,x=0$

∴ The value of x = 0