Question:
Which expression is equivalent to ³√(216x³y⁶z¹²)
Answer:
A. 6xy²z⁴
Step-by-step explanation:
Given
³√(216x³y⁶z¹²)
Required
Simplify
The above expression can be simplified by following the steps below
1. Expand the expression with multiplication sign
³√(216 * x³ * y⁶ * z¹²)
2. From laws of indices,
√ab = √a * √b.
So, the above expression can also be splitted as follows
(³√216 ) * (³√x³) * (³√y⁶) * (³√z¹²)
3. From laws of indices,
ⁿ√a = a^¹/ⁿ
So, the above expression can be rewritten as
(216)^⅓ * (x³)^⅓ * (y⁶)^⅓ * (z¹²)^⅓
= (6*6*6)^⅓ * (x³)^⅓ * (y⁶)^⅓ * (z¹²)^⅓
= (6³)^⅓ * (x³)^⅓ * (y⁶)^⅓ * (z¹²)^⅓
Multiplying the powers; this will give us
= 6 * x * y² * z⁴
= 6xy²z⁴
Hence, the equivalent of ³√(216x³y⁶z¹²) is 6xy²z⁴
