Rewrite the expression ith a positive rational exponent. 256^-3/4=

256 ^ -3/4

law of exponents; to the power of a negative, flip the fraction and make power positive

(256/1) ^ -3/4

(1/256) ^3/4

which in radical form is like this:

^4√(1/256)^3

^4√(1/16 777 216)

= 1/64

which can be written as an expression of powers

= 1/(8x8)

= 1/(2^3 x 2^3)

= 1/(2^6)

256^-3/4 =
1 / (256^3/4) =
1 / 4th root(256^3)
1 / 4th root(16777216)
1 / 64 =

(1/8)^2 or (1/4)^3 or (1/2)^6