Answer: 4a²b⁴c³
Explanation:
To simplify the expression ∛(256a⁶b¹²c⁹), you can find the cube root of each factor individually:
∛256 = 4 because 4³ = 64, and 256 is 4 times 64.
∛a⁶ = a² because (a²)³ = a⁶.
∛b¹² = b⁴ because (b⁴)³ = b¹².
∛c⁹ = c³ because (c³)³ = c⁹.
Now, combine these results:
∛(256a⁶b¹²c⁹) = ∛256 * ∛a⁶ * ∛b¹² * ∛c⁹ = (4 * a² * b⁴ * c³) = 4a²b⁴c³
So, the simplified expression is 4a²b⁴c³.