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 drop - down menu with 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

$\sqrt{200x^{13}}=\sqrt{4\cdot25\cdot2\cdot(x^6)^2\cdot x}$, $\sqrt{32x^7}=\sqrt{16\cdot2\cdot(x^3)^2\cdot x}$ (correct factoring)

Step2: Check Step 2 simplification

$\sqrt{4\cdot25\cdot2\cdot(x^6)^2\cdot x}=2\cdot5\cdot x^6\sqrt{2x}=10x^6\sqrt{2x}$, so $8x^6\sqrt{200x^{13}}=8x^6\cdot10x^6\sqrt{2x}=80x^{12}\sqrt{2x}$ (correct for first term). For the second term: $\sqrt{16\cdot2\cdot(x^3)^2\cdot x}=4\cdot x^3\sqrt{2x}$, so $2x^5\sqrt{32x^7}=2x^5\cdot4x^3\sqrt{2x}=8x^8\sqrt{2x}$. Seth incorrectly used $16$ instead of $4$ here.

Step3: Identify the error

Seth miscalculated the square root of 16 as 16 instead of 4, leading to wrong coefficient in Step 2.

Answer:

factored 16 out of the second term instead of 4