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What is the following product? Assume x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0

StartRoot 5 x Superscript 8 Baseline y squared EndRoot times StartRoot 10 x cubed EndRoot times StartRoot 12 y EndRoot
3 x Superscript 5 Baseline y StartRoot 3 x y EndRoot
10 x Superscript 5 Baseline y StartRoot 6 x y EndRoot
3 x cubed y StartRoot 3 x squared y squared EndRoot
10 x cubed y StartRoot 6 x squared y squared EndRoot

What is the following product Assume x greaterthanorequalto 0 and y greaterthanorequalto 0 StartRoot 5 x Superscript 8 Baseline y squared EndRoot times StartRoo class=

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TheAnimeGirl

[tex]answer \\ = 10 {x}^{5} y \sqrt{6xy} \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps[/tex]

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The product of the given expression is;

B: 10x^(5) • y√(6xy)

Laws of Exponents

We are given the expression;

√(5x^(8) • y²) × √(10x³) × √(12y)

Now, according to laws of exponents, we know that; √(a⁴) × √(b³) = √(a⁴ × b³)

Thus, our given expression will be;

√(5x^(8) • y²) × √(10x³) × √(12y) = √[(5x^(8) • y²) × (10x³) × (12y)]

  • Collecting like terms, we will have;

√[(5x^(8) × 10x³) × (y² × 12y)]

  • This now gives;

√(50x¹¹ × 12y³)

>> √(600x¹¹y³)

Now, further break down of this gives;

10x^(5) • y√(6xy)

Read more about Laws of exponents at; https://brainly.com/question/11761858

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