Question

The number $(1024{)}^{1024}$ is obtained by raising $(16{)}^{16}$ to the power $n$. What is the value of $n$?

• A. $64$
• B. $(64{)}^2$
• C. $(64{)}^{64}$
• D. $160$

Answer 1

The correct option is D $160$

$(1024{)}^{1024}=(16{)}^{16}{)}^n$
$\Rightarrow (2^{10}{)}^{1024}=(16{)}^{16n}$
$\Rightarrow (2{)}^{10240}=(2^4{)}^{16n}$
$\Rightarrow (2{)}^{10240}=(2{)}^{64n}$
$\Rightarrow 64n=10240$
$\Rightarrow n=160$
Option D is correct.