Final answer:
To simplify ((2u³v)/(w⁻¹))⁻³(u⁻²w⁶), first convert all negative powers to positive, simplify the fractions, and multiply remaining terms. The final simplified form is 1/(8u⁷v³w⁹).
Step-by-step explanation:
To simplify the given expression, ((2u³v)/(w⁻¹))⁻³(u⁻²w⁶), we must first convert any negative powers to positive powers. This can be done by flipping the fraction they are attached to. Therefore, (w⁻¹) becomes 1/w, and (u⁻²) becomes 1/(u²).
So, the transformed expression is ((2u³v)*(w))/(1/((1/u²)*w⁶)), which simplifies to (2u³vw)^-³*(u²/w⁶).
Applying the power of -3, results in 1/(2u³vw)³ = 1/(8u⁹v³w³).
Multiplying the result by (u²/w⁶), we get (u²/w⁶)/(8u⁹v³w³) which further simplifies to 1/(8u⁷v³w⁹) as the final answer. This is because u² in the numerator and u⁹ from 8u⁹v³w³ in the denominator simplifies to u⁷. Similarly, w⁶ in the numerator and w³ from 8u⁹v³w³ in the denominator simplifies to w⁹.
Learn more about Simplifying Mathematical Expressions