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Answer :
Let's review the steps carefully to identify where Seth made a mistake.
Step 1:
Seth rewrote the expression by breaking down the square roots:
[tex]\[ 8x^6 \sqrt{200x^{13}} \div 2x^5 \sqrt{32x^7} \][/tex]
Step 2:
Seth factored the numbers inside the square roots:
[tex]\[ 8x^6 \sqrt{4 \cdot 25 \cdot 2 \cdot (x^6)^2 \cdot x} \div 2x^5 \sqrt{16 \cdot 2 \cdot (x^3)^2 \cdot x} \][/tex]
Step 3:
Seth simplified the square roots and the expression as:
[tex]\[ 80x^{12} \sqrt{2x} \div 32x^8 \sqrt{2x} \][/tex]
Step 4:
Here, Seth made a mistake. The expression was simplified to:
[tex]\[ \frac{80x^{11} \sqrt{2x}}{32x^5 \sqrt{2x}} \][/tex]
The mistake is here. Seth incorrectly divided the powers of [tex]\(x\)[/tex]. When dividing [tex]\(x^{12}\)[/tex] by [tex]\(x^8\)[/tex], it should result in [tex]\(x^4\)[/tex], not [tex]\(x^{11}\)[/tex].
Step 5:
Despite the mistake in Step 4, Seth provided a final answer:
[tex]\[ \frac{5}{2}x^4 \][/tex]
So, Seth's first mistake was in Step 4, where he incorrectly calculated the division of the powers of [tex]\(x\)[/tex]. The correct division should have resulted in [tex]\(x^4\)[/tex].
Step 1:
Seth rewrote the expression by breaking down the square roots:
[tex]\[ 8x^6 \sqrt{200x^{13}} \div 2x^5 \sqrt{32x^7} \][/tex]
Step 2:
Seth factored the numbers inside the square roots:
[tex]\[ 8x^6 \sqrt{4 \cdot 25 \cdot 2 \cdot (x^6)^2 \cdot x} \div 2x^5 \sqrt{16 \cdot 2 \cdot (x^3)^2 \cdot x} \][/tex]
Step 3:
Seth simplified the square roots and the expression as:
[tex]\[ 80x^{12} \sqrt{2x} \div 32x^8 \sqrt{2x} \][/tex]
Step 4:
Here, Seth made a mistake. The expression was simplified to:
[tex]\[ \frac{80x^{11} \sqrt{2x}}{32x^5 \sqrt{2x}} \][/tex]
The mistake is here. Seth incorrectly divided the powers of [tex]\(x\)[/tex]. When dividing [tex]\(x^{12}\)[/tex] by [tex]\(x^8\)[/tex], it should result in [tex]\(x^4\)[/tex], not [tex]\(x^{11}\)[/tex].
Step 5:
Despite the mistake in Step 4, Seth provided a final answer:
[tex]\[ \frac{5}{2}x^4 \][/tex]
So, Seth's first mistake was in Step 4, where he incorrectly calculated the division of the powers of [tex]\(x\)[/tex]. The correct division should have resulted in [tex]\(x^4\)[/tex].
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