Question

root 2 to the power x is equals to 2 to the power 8

Answer 1

$\bold{Answer:}$

$x = \bold{16}$

$\bold{Step} - \bold{by} - \bold{step\ explanation:}$

$(\sqrt{2})^x = 2^8 \\ \\ (2^{\frac{1}{2}})^x = 2^8 \\ \\ 2^{\frac{1}{2} \times x} = 2^8 \\ \\ 2^{\frac{x}{2}} = 2^8 \\ \\ \\ \frac{x}{2} = 8 \\ \\ x = 8 \times 2 = \bold{16}$

$\therefore\ x = \bold{16}$

Answer 2

2 can be written as √2×√2
2 to the power 8=(√2×√2) to the power 8
=[(√2)²] to the power 8
=(√2) to the power 16
(√2) to the power x=√2 to the power 16
=>x=16