Question

What is the cube root of 64x^12

Answer 1

64x^12 = 4^3 x^12
cube root 64x^12  =  4x^4

answer 4x^4

Answer 2

Answer:  The required cube root of the given expression is $4x^4.$

Step-by-step explanation:  We are given to find the cube root of the following expression :

$E=64x^{12}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~``(i)$

We will be using the following property :

$\sqrt[n]{a}=a^\frac{1}{n}.$

Taking cube root on both sides of equation (i), we get

$\sqrt[3]E\\\\=\sqrt[3]{64x^{12}}\\\\=(64x^{12})^\frac{1}{3}\\\\=(4^3x^{12})^\frac{1}{3}\\\\=4^{3\times\frac{1}{3}}x^{12\times\frac{1}{3}}}\\\\=4x^4.$

Thus, the required cube root of the given expression is $4x^4.$