Question

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

Answer 1

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

Explanation:

Answer 2

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 * 3 * 3 * \mathrm{a}^(12)} \\\\ {27 \mathrm{a}^(12)=3 * 3 * 3 * \mathrm{a}^(4 * 3)}\end{array}`

Using law of exponents
`a^(m * n)=\left(a^(m)\right)^(n)`

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

Thus the cube root of 27a^12 is
`=3 a^(4)` Hence option D is correct