Question 390812
((4)^(-3))/(4x)=(1)/(2)

Expand the exponent (3) to the expression.
(1)/(4^(3))*(1)/(4x)=(1)/(2)

Cubing a number is the same as multiplying the number by itself 3 times (4*4*4).  In this case, 4 cubed is 64.
(1)/(64)*(1)/(4x)=(1)/(2)

Multiply (1)/(64) by (1)/(4x) to get (1)/(256x).
(1)/(256x)=(1)/(2)

Since there is one rational expression on each side of the equation, this can be solved as a ratio.  For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
1*2=1*256x

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
1*256x=1*2

Multiply 1 by 256x to get 256x.
256x=1*2

Multiply 1 by 2 to get 2.
256x=2

Divide each term in the equation by 256.
(256x)/(256)=(2)/(256)

Simplify the left-hand side of the equation by canceling the common factors.
x=(2)/(256)

Simplify the right-hand side of the equation by simplifying each term.
x=(1)/(128)