Respuesta :

[tex]\bf \sqrt[3]{27a^3b^7}\quad \begin{cases} 27=3\cdot 3\cdot 3\\ \qquad 3^3\\ b^7=b^{3+3+1}\\ \qquad b^3b^3b^1\\ \qquad (b^2)^3b^1 \end{cases}\implies \sqrt[3]{3^3a^3(b^2)^3b^1} \\\\\\ 3ab^2\sqrt[3]{b^1}\implies 3ab^2\sqrt[3]{b}[/tex]

Answer:

Option (a) is correct.

The simplified form of  [tex]\sqrt[3]{27a^3b^7}[/tex] is [tex]3ab^2\sqrt[3]{b}[/tex]

Step-by-step explanation:

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

We have to write the simplest form of given expression [tex]\sqrt[3]{27a^3b^7}[/tex]        

Consider the given expression  [tex]\sqrt[3]{27a^3b^7}[/tex]

27 can be written as 3³

[tex]b^7[/tex] can be written as [tex]b^3b^3b[/tex]

Thus, expression becomes,

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

Thus, Simplify, we get,

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

Thus, The simplified form of  [tex]\sqrt[3]{27a^3b^7}[/tex] is [tex]3ab^2\sqrt[3]{b}[/tex]

Otras preguntas