(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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

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