Final answer:
The simplified expression of ((-3w²)/(v))⁴ is 81w⁸/v⁴, obtained by raising each term in the fraction to the fourth power separately.
Step-by-step explanation:
To simplify the expression ((-3w²)/(v))⁴ without parentheses, raise each element in the fraction to the fourth power separately. Raising a power to another power means you multiply the exponents, and remember that the negative sign will become positive since an even power negates the negative sign.
- (-3)⁴ = 81 because (-3) x (-3) x (-3) x (-3) = 81,
- (w²)⁴ = w⁸ because 2 x 4 = 8,
- (v)⁴ = v⁴ because 1 x 4 = 4.
So, the final simplified expression is 81w⁸/v⁴.