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

Explanation:

Step1: Expand numerator via power rule

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

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 sign for positive form

Since the result has a negative coefficient, we can write it as $-64n^{13}$ (positive exponents are already satisfied)

Answer:

$-64n^{13}$