Final answer:
To simplify (5n⁴)⁻³, rewrite it as 1/(5³ * (n⁴)³) and simplify to 1/(125 * n^12).
Step-by-step explanation:
To simplify (5n⁴)⁻³, we need to apply the exponent rule which states that when you have a power raised to a negative exponent, you can rewrite it as the reciprocal of the base raised to the positive exponent. In this case, the base is 5n⁴ and the exponent is -3. So we can rewrite the expression as 1/(5n⁴)³.
Now, we can apply the power rule of exponents. Since the exponent 3 is applied to both the 5 and the n⁴ separately, we can rewrite it as 1/(5³ * (n⁴)³). Which simplifies to 1/(125 * n^(4*3)). Finally, we can simplify this further to 1/(125 * n^12).