Final answer:
To simplify the expression ((z⁴)/(3y³))⁵, we apply the rule of raising a power to a power and multiply the exponents of the variables. The simplified expression is z^20 / (3^5)*(y^15).
Step-by-step explanation:
To simplify the expression, ((z⁴)/(3y³))⁵, we can apply the rule of raising a power to a power. To do this, we multiply the exponents of the variables. In this case, the exponent of z⁴ is multiplied by 5, and the exponent of 3y³ is also multiplied by 5. This gives us (z⁴)⁵ / (3y³)⁵.
Next, we simplify each term by raising it to the power of 5. For the numerator, (z⁴)⁵ becomes z^(4*5) which is z^20. For the denominator, (3y³)⁵ becomes (3^(5))*(y^(3*5)), which is (3^5)*(y^15).
Therefore, the simplified expression is z^20 / (3^5)*(y^15).