Question

select the correct answer from each drop - down menu. review seths steps for rewriting and simplifying an expression. given $8x^{6}sqrt{200x^{13}}div2x^{5}sqrt{32x^{7}}$ 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 $=\frac{5}{2}x^{4}$ seths first mistake was made in step 2, where he factored 16 out of the second term instead of 4 (options: 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 rewrite the expression as division correctly)

Explanation:

Step1: Analyze Step 1 factoring

For the second radical $\sqrt{32x^7}$, $32=16\times2$, $\sqrt{16}=4$, so $\sqrt{32x^7}=4x^3\sqrt{2x}$.

Step2: Check Step 2 execution

Seth incorrectly used $\sqrt{16}=16$ instead of $\sqrt{16}=4$ for the second term, writing $2\cdot16\cdot x^5\cdot x^3\sqrt{2x}$ instead of $2\cdot4\cdot x^5\cdot x^3\sqrt{2x}$.

Step3: Match error to options

This error matches "factored 16 out of the second term instead of 4".

Answer:

Seth's first mistake was made in Step 2, where he factored 16 out of the second term instead of 4.