The completed statement is as follows;
Seth's first mistake was made in Step 2, where he factored 16 out of the second term instead of 4
The expression 8·x⁶·√(200·x¹³) ÷ 2·x⁵·√(32·x⁷) can be simplified as follows;
8·x⁶·√(200·x¹³) ÷ 2·x⁵·√(32·x⁷) = 8·x⁶·√(4·25·2·(x⁶)²·x) ÷ 2·x⁵·√(16·2·(x³)²·x)
8·x⁶·√(4·25·2·(x⁶)²·x) ÷ 2·x⁵·√(16·2·(x³)²·x) = 8·x⁶·√(2²·5²·2·(x⁶)²·x) ÷ 2·x⁵·√(4²·2·(x³)²·x)
Therefore; 8·x⁶·√(4·25·2·(x⁶)²·x) ÷ 2·x⁵·√(16·2·(x³)²·x) = 8·x⁶·2·5·x⁶√(2·x) ÷ 2·x⁵·4·x³·√(2·x)
However in step 1 and step 2, we get;
Step 1 = 8·x⁶·√(4·25·2·(x⁶)²·x) ÷ 2·x⁵·√(16·2·(x³)²·x)
Step 2 = 8 · 2 · 5 · x⁶ · x⁶ · √(2·x) ÷ 2 · 16 · x⁵ ·x³ · √(2·x)
The correct expression for Step 2 is therefore;
8·x⁶·2·5·x⁶√(2·x) ÷ 2·x⁵·4·x³·√(2·x) = 8·2·5·x⁶·x⁶·√(2·x) ÷ 2·4·x⁵·x³·√(2·x)
The first mistake is made in Step 2, where the square root of 16 is taken as 16
Further simplification, we get;
8·2·5·x⁶·x⁶·√(2·x) ÷ 2·4·x⁵·x³·√(2·x) = 80·x¹² ÷ 8·x⁸
80·x¹² ÷ 8·x⁸ = 10·x⁴
The possible options, to be used to complete the statements obtained from a similar question found through search are;
Factored 16 out of the second term instead of 4
Did not apply the properties of exponents correctly
Factored 2 out of the first term instead of 4
Did not write the expression as division correctly