Question

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review seth’s steps for rewriting and simplifying an expression.
given (\boldsymbol{8x^{6}sqrt{200x^{13}}div2x^{5}sqrt{32x^{7}}})
step 1 (= 8x^{6}sqrt{4cdot25cdot2cdot(x^{6})^{2}cdot x}div2x^{5}sqrt{16cdot2cdot(x^{3})^{2}cdot x})
step 2 (= 8cdot2cdot5cdot x^{6}cdot x^{6}sqrt{2x}div2cdot16cdot x^{5}cdot x^{3}sqrt{2x})
step 3 (= 80x^{12}sqrt{2x}div32x^{8}sqrt{2x})
step 4 (=\frac{80x^{12}sqrt{2x}}{32x^{8}sqrt{2x}})
step 5 (=\frac{5}{2}x^{4})
seth’s first mistake was made in (\boldsymbol{square}), where he (\boldsymbol{square})

Explanation:

Step1: Analyze Step1 factorization

$8x^6\sqrt{4 \cdot 25 \cdot 2 \cdot (x^6)^2 \cdot x} \div 2x^5\sqrt{16 \cdot 2 \cdot (x^3)^2 \cdot x}$

Step2: Check Step2 simplification

Correct simplification: $8x^6 \cdot 2 \cdot 5 \cdot x^6\sqrt{2x} \div 2x^5 \cdot 4 \cdot x^3\sqrt{2x}$

Step3: Identify error in Step2

Seth incorrectly simplified $\sqrt{16}$ as $16$ instead of $4$.

Step4: Verify subsequent steps

The error propagates, but first error is Step2.

Answer:

Seth's first mistake was made in Step 2, where he incorrectly calculated $\sqrt{16}$ as $16$ instead of $4$.