find the value

We have,

$10^{x}=64$

Taking square root from both sides, we get

$\sqrt{10^{x}}=\sqrt{64}$

$\Rightarrow\left(10^{x}\right)^{\frac{1}{2}}=8$

$\Rightarrow 10^{\left(\frac{x}{2}\right)}=8$

Multiplying both sides by 10 , we get

$10^{\left(\frac{x}{2}\right)} \times 10=8 \times 10$

$\therefore 10^{\left(\frac{x}{2}+1\right)}=80$