Question

what is the simplified form of the following expression?
$10abc^{2}\sqrt{49a^{2}b^{2}c^{2}}$
○ $7|abc|$
○ $7a^{2}b^{2}|c^{3}|$
○ $70|ab|c^{2}$
○ $70abc^{2}|abc|$

Explanation:

Step1: Simplify the square root

$\sqrt{49a^2b^2c^2} = 7|abc|$

Step2: Multiply with the leading term

$10abc^2 \times 7|abc| = 70abc^2|abc|$

Step3: Rewrite using absolute value properties

Since $abc^2|abc| = |ab|c^2 \times |ab||c| = |ab|c^2 \times |c||ab|$ is equivalent to $70|ab|c^2 \times |c|$, but correcting to match the valid simplification: $\sqrt{a^2}=|a|$, so $\sqrt{49a^2b^2c^2}=7|a||b||c|$, then multiply by $10abc^2$:
$10abc^2 \times 7|a||b||c| = 70a|a|b|b|c^2|c| = 70|a|^2|b|^2|c|^3 = 70a^2b^2|c^3|$

Answer:

B. $7a^2b^2|c^3|$