High School

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Review Seth's steps for rewriting and simplifying an expression.

Given: [tex]8 x^6 \sqrt{200 x^{13}} \div 2 x^5 \sqrt{32 x^7}[/tex]

Step 1: [tex]8 x^6 \sqrt{4 \cdot 25 \cdot 2 \cdot (x^6)^2 \cdot x} \div 2 x^5 \sqrt{16 \cdot 2 \cdot (x^3)^2 \cdot x}[/tex]

Step 2: [tex]8 \cdot 2 \cdot 5 \cdot x^6 \cdot x^6 \sqrt{2 x} \div 2 \cdot 16 \cdot x^5 \cdot x^3 \sqrt{2 x}[/tex]

Step 3: [tex]80 x^{12} \sqrt{2 x} \div 32 x^8 \sqrt{2 x}[/tex]

Step 4: [tex]\frac{80 x^{12} \sqrt{2 x}}{32 x^8 \sqrt{2 x}}[/tex]

Step 5: [tex]\frac{5}{2} x^4[/tex]

Seth's first mistake was made in [tex]\square[/tex], where he [tex]\square[/tex].

Answer :

Seth's first mistake was made in Step 2, where he incorrectly simplified the constants.

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