1/64=16^2a

Solution for 1/64=16^2a equation:

1/64=16^2a

We move all terms to the left:

1/64-(16^2a)=0

We multiply all the terms by the denominator


-16^2a*64+1=0

Wy multiply elements

-1024a^2+1=0

a = -1024; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1024)·1
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64}{2*-1024}=\frac{-64}{-2048}
=1/32
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64}{2*-1024}=\frac{64}{-2048}
=-1/32
$