Answer:
Cube-root defines: A number is a special value that, when used in a multiplication three times, gives that number.
Its symbol is denoted by: [tex]\sqrt[3]{}[/tex]
USing Law of radical:
1. [tex]\sqrt[n]{ab}= \sqrt[n]{a} \cdot \sqrt[n]{b}[/tex]
2. [tex]\sqrt[n]{x^n} =(\sqrt[n]{x} )^n =\sqrt[n]{x^n} =x[/tex]
To find the cube root of [tex]27a^{12}[/tex] ;
By the definition of cube root
[tex]\sqrt[3]{27 a^{12}}[/tex] = [tex]\sqrt[3]{27} \cdot \sqrt[3]{a^{12}}[/tex] [Using [1]]
we can write 27 as [tex]3 \times 3 \times 3 = 3^3[/tex] and [tex]a^{12} = (a^4)^3[/tex]
then;
[tex]\sqrt[3]{27 a^{12}}[/tex] = [tex]\sqrt[3]{3^3} \cdot \sqrt[3]{a^{4}^3}[/tex]
= [tex]3 \cdot a^4[/tex] [ Using [2] ]
therefore, the cube root of [tex]27a^{12}[/tex] is [tex]3a^4[/tex]
