Question

What is the cube root of 27a^12? A. -за^ B.-За C.За D.за^4

Answer 1

Answer:

Cube root of 27 a^12 will be: D 3 a^4.

Step-by-step explanation:

Answer 2

Answer:

The cube root of 27a^12 is $=3 a^{4}$ Hence option D is correct

Solution:

Given that $27 \mathrm{a}^{12}$

Need to determine cube root of $27 \mathrm{a}^{12}$

$\text { Lets factorize } 27 \mathrm{a}^{12}$

$\begin{array}{l}{27 \mathrm{a}^{12}=3 \times 3 \times 3 \times \mathrm{a}^{12}} \\\\ {27 \mathrm{a}^{12}=3 \times 3 \times 3 \times \mathrm{a}^{4 \times 3}}\end{array}$

Using law of exponents $a^{m \times n}=\left(a^{m}\right)^{n}$

$\begin{array}{l}{27 \mathrm{a}^{12}=3 \times 3 \times 3 \times \left(\mathrm{a}^{4}\right)^{3}} \\\\ {27 \mathrm{a}^{12}=3 \times 3 \times 3 \times \mathrm{a}^{4} \times \mathrm{a}^{4} \times \mathrm{a}^{4}} \\\\ {\sqrt[3]{27 a^{12}}=\sqrt[3]{3 \times 3 \times 3 \times a^{4} \times a^{4} \times a^{4}}} \\\\ {=>\sqrt[3]{27 a^{12}}=3 \times a^{4}=3 a^{4}}\end{array}$

Thus the cube root of 27a^12 is $=3 a^{4}$ Hence option D is correct