Question

Which expression is equivalent to cbrt 3√216x³y⁶z¹²?

A. 6xy²z⁴
B. 18xy³z⁶
C. 36xy²z⁴
D. 72xy³z⁶

Answer 1

The equivalent expression of the cube root of 3∙216x³y⁶z¹² is 6xy2z4, obtained by simplifying each factor under the cube root separately.

Step-by-step explanation:

The student is asking for the equivalent expression of the cube root of 3∙216x³y⁶z¹². To simplify this expression, we should recognize that 216 is a perfect cube since 216 = 63. We can then rewrite the expression under the cube root as (63x3y6z12), and then take the cube root of each factor separately. Here is the breakdown:

• The cube root of 63 is 6, because ∙63 = 6.
• The cube root of x3 is x, because ∙x3 = x.
• The cube root of y6 is y2, because ∙y6 = y2.
• The cube root of z12 is z4, because ∙z12 = z4.

Thus, the expression simplifies to 6xy2z4, which is option A.