Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{(-4n^{5})^{4}}{-4n^{7}}\\)

Explanation:

Step1: Expand numerator via exponent rules

$(-4n^5)^4 = (-4)^4 \cdot (n^5)^4 = 256n^{20}$

Step2: Rewrite the original fraction

$\frac{256n^{20}}{-4n^7}$

Step3: Simplify coefficients and exponents

$\frac{256}{-4} \cdot n^{20-7} = -64n^{13}$

Step4: Adjust for positive exponents (already satisfied)

No further changes needed, as $n^{13}$ has a positive exponent.

Answer:

$-64n^{13}$