Express in simplest radical form. \[ 8 x \sqrt{10 x^{2}}-7 \sqrt{10 x^{4}} \]

To simplify the expression \( 8 x \sqrt{10 x^{2}} - 7 \sqrt{10 x^{4}} \), let's break it down step by step. First, simplify each radical term. 1. The first term: \[ 8x \sqrt{10x^2} = 8x \cdot \sqrt{10} \cdot \sqrt{x^2} = 8x \cdot \sqrt{10} \cdot x = 8x^2 \sqrt{10} \] 2. The second term: \[ -7 \sqrt{10x^4} = -7 \cdot \sqrt{10} \cdot \sqrt{x^4} = -7 \cdot \sqrt{10} \cdot x^2 = -7x^2 \sqrt{10} \] Now we can combine the two terms: \[ 8x^2 \sqrt{10} - 7x^2 \sqrt{10} = (8 - 7)x^2 \sqrt{10} = 1x^2 \sqrt{10} = x^2 \sqrt{10} \] Thus, the expression in simplest radical form is: \[ \boxed{x^2 \sqrt{10}} \]