Final answer:
The expression ((5xy⁴)/(x³y))⁻³ simplifies to 1/(5³x⁶y), following the rules of division and negative exponents.
Step-by-step explanation:
To simplify the expression ((5xy⁴)/(x³y))⁻³, we need to follow the rules of exponents for division and negative powers. First, we divide the coefficients (5/1 in this case) and subtract the exponents of the variables. For the x terms, we have x to the power of 1 in the numerator and x to the power of 3 in the denominator, so we subtract the exponents (1 - 3 = -2). For the y terms, we have y to the power of 4 in the numerator and y to the power of 1 in the denominator, so we subtract these exponents as well (4 - 1 = 3). This gives us (5x⁻²y³).
Next, we apply the negative power, which means we take the reciprocal of the base and change the sign of the exponent. Raising this to the power of -3 means each factor's exponent is multiplied by -3. The simplified expression is (5⁻³x⁶y⁻¹), which is the same as 1/(5³x⁶y).