Unproctored Placement Assessment
Question 22
Simplify.
$$
\sqrt{6 y^{6} w^{7}} \sqrt{2 y^{3} w^{4}}
$$

Assume that all variables represent positive real numbers.
$\square$
$\square$
$$
\sqrt{\square}
$$
$$
\square
$$

Question

Unproctored Placement Assessment
Question 22
Simplify.
$$
\sqrt{6 y^{6} w^{7}} \sqrt{2 y^{3} w^{4}}
$$

Assume that all variables represent positive real numbers.
$\square$
$\square$
$$
\sqrt{\square}
$$
$$
\square
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Start with the given expression: $\sqrt[6]{6y^6w^7} \cdot \sqrt{2y^3w^4}$ ‖ ‖ step 2 ⋮ Rewrite the expression using fractional exponents: $(6y^6w^7)^{1/6} \cdot (2y^3w^4)^{1/2}$ ‖ ‖ step 3 ⋮ Simplify each term separately: $(6^{1/6} \cdot y \cdot w^{7/6}) \cdot (2^{1/2} \cdot y^{3/2} \cdot w^2)$ ‖ ‖ step 4 ⋮ Combine the constants: $6^{1/6} \cdot 2^{1/2}$ ‖ ‖ step 5 ⋮ Combine the $y$ terms: $y \cdot y^{3/2} = y^{1 + 3/2} = y^{5/2}$ ‖ ‖ step 6 ⋮ Combine the $w$ terms: $w^{7/6} \cdot w^2 = w^{7/6 + 12/6} = w^{19/6}$ ‖ ‖ step 7 ⋮ Combine all parts: $6^{1/6} \cdot 2^{1/2} \cdot y^{5/2} \cdot w^{19/6}$ ‖ ∻Answer∻ ⚹ $6^{1/6} \cdot 2^{1/2} \cdot y^{5/2} \cdot w^{19/6}$ ⚹ ∻Key Concept∻ ⚹Simplification of radical expressions⚹ ∻Explanation∻ ⚹The key to simplifying this expression is to convert the radicals to fractional exponents and then combine like terms.⚹◊What is the final simplified expression for $ \sqrt{6y^{6}w^{7}} imes \sqrt{2y^{3}w^{4}}⍭ Generate me a similar question◊

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