(x^3*x^-7/x^2)^ 1/4=1/8 than x = A. .5 B.1.0 C.4.0 D.32.0 E.72.5

When multiply two exponentials that have the same base,
the superscripts are added.

x^3*x^-7 = x^(3+(-7)) =
x^(-4)

When we perform the divison of two exponentials with
the same bases, we subtract the exponent of denominator from the exponent of
numerator:

x^3*x^(-7)/x^2 = x^(-4)/x^2 = x^(-4-2) =
x^(-6)

When we raise an exponential to a power, we'll
multiply the exponents:

[x^(-6)]^(1/4) = x^[-6*(1/4)] =
x^(-6/4) = x^(-3/2)

Now, we'll apply the negative power
rule:

a^-b = 1/a^b

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

We'll put 1/x^(3/2) = 1/8. By cross multiplying,
we'll get:

x^(3/2) = 8

We'll
raise both sides to 2/3, to get x:

[x^(3/2)]^(2/3) =
8^(2/3)

x = cube root (8^2)

x
= 4

The correct answer is C: x =
4.0