Respuesta :

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[tex]\displaystyle\\ \sqrt[3]{27a^3b^7} =\sqrt[3]{3^3 a^3b^6\times b} =\sqrt[3]{3^3 a^3\Big(b^2\Big)^3\times b} = \boxed{\bf 3ab^{\b2} \sqrt[\b 3]{\bf b} }\\\\ \text{Correct ansver: a)}[/tex]

Answer:

Option a -  [tex]\sqrt[3]{27a^3b^7}==3ab^2\sqrt[3]{b}[/tex]

Step-by-step explanation:

Given : Expression [tex]\sqrt[3]{27a^3b^7}[/tex]

To find : What is the simplest form of expression ?

Solution :

Step 1 - Write the expression

[tex]\sqrt[3]{27a^3b^7}[/tex]

Step 2 - Split the term into their factor,

[tex]27=3^3[/tex]

[tex]b^7=b^3b^3b[/tex]

Step 3 - Re-write the expression,

[tex]\sqrt[3]{27a^3b^7}=\sqrt[3]{3^3a^3b^6b^3b}[/tex]

Step 4 - Simplify the expression

[tex]\sqrt[3]{27a^3b^7}==3ab^2\sqrt[3]{b}[/tex]

Therefore, Option a is correct.

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