Question

What is the simplest form of ^3 square root 27a^3b^7

Answer 1

Answer:

Option (a) is correct.

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

Step-by-step explanation:

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

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

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

27 can be written as 3³

$b^7$ can be written as $b^3b^3b$

Thus, expression becomes,

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

Thus, Simplify, we get,

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

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

Answer 2

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