Question

✓2 to the power n =1024 then find the value of 1024 power 2/5

Answer 1

Answer:

16

Step-by-step explanation:

Writing it down,

$\sqrt{2}^{n}=1024\\ 2^{n/2}=1024\\ 2^{n/2}=2^10\\\frac{n}{2}=10\\n=20$

Further,

$1024^{2/5} = (2^{10})^{2/5}$

When raising a power to another power, the indices multiply.

$=2^{10*\frac{2}{5}}\\=2^{2*2}\\=2^4\\=16$