8. \( \frac{7\left(x^{4}\right)^{3}}{\left(3 x^{2}\right)^{2}} \)

To simplify the expression \( \frac{7\left(x^{4}\right)^{3}}{\left(3 x^{2}\right)^{2}} \), we'll start with the numerator and denominator separately. In the numerator, we have \( 7\left(x^{4}\right)^{3} = 7x^{12} \) (because \( (x^4)^3 = x^{4 \cdot 3} = x^{12} \)). In the denominator, we compute \( (3x^{2})^{2} = 9x^{4} \) (since \( (3)^2 = 9 \) and \( (x^{2})^2 = x^{4} \)). Now, substituting back, we get: \[ \frac{7x^{12}}{9x^{4}} \] Next, we can simplify this by dividing the coefficients and subtracting the exponents: \[ \frac{7}{9} x^{12 - 4} = \frac{7}{9} x^{8} \] So, the simplified expression is: \[ \frac{7}{9} x^{8} \] And there you have it, simplified and ready to go!