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: \(\sqrt[3]{}\)
USing Law of radical:
1. \(\sqrt[n]{ab}= \sqrt[n]{a} \cdot \sqrt[n]{b}\)
2. \(\sqrt[n]{x^n} =(\sqrt[n]{x} )^n =\sqrt[n]{x^n} =x\)
To find the cube root of \(27a^{12}\) ;
By the definition of cube root
\(\sqrt[3]{27 a^{12}}\) = \(\sqrt[3]{27} \cdot \sqrt[3]{a^{12}}\) [Using [1]]
we can write 27 as \(3 \times 3 \times 3 = 3^3\) and \(a^{12} = (a^4)^3\)
then;
\(\sqrt[3]{27 a^{12}}\) = \(\sqrt[3]{3^3} \cdot \sqrt[3]{a^{4}^3}\)
= \(3 \cdot a^4\) [ Using [2] ]
therefore, the cube root of \(27a^{12}\) is \(3a^4\)
