Express the following fraction in simplest form, only using positive exponents. (-3(j^-3a^4)^-3)/(3j^4)a^(8) Answer Attemptiout of 2 square

To simplify the given fraction $\frac{-3(j^{-3}a^{4})^{-3}}{3j^{4}a^{8}}$, we need to follow these steps:

1. Simplify the expression in the numerator: $(j^{-3}a^{4})^{-3}$.

Applying the power of a power property, $(x^m)^n = x^{m \cdot n}$, we get:
$$(j^{-3}a^{4})^{-3} = j^{-3 \cdot (-3)}a^{4 \cdot (-3)} = j^{9}a^{-12}$$

2. Substitute back into the original fraction:
$$\frac{-3(j^{9}a^{-12})}{3j^{4}a^{8}}$$

3. Simplify the fraction by canceling common factors and applying the properties of exponents:

- The coefficient $-3$ in the numerator and $3$ in the denominator can be simplified:
$$\frac{-3}{3} = -1$$

- For the $j$ terms:
$$\frac{j^{9}}{j^{4}} = j^{9-4} = j^{5}$$

- For the $a$ terms:
$$\frac{a^{-12}}{a^{8}} = a^{-12-8} = a^{-20}$$

4. Combine the results:
$$-1 \cdot j^{5} \cdot a^{-20} = -j^{5}a^{-20}$$

5. Express using only positive exponents:
$$-j^{5} \cdot \frac{1}{a^{20}} = -\frac{j^{5}}{a^{20}}$$

Thus, the simplest form of the given fraction is $-\frac{j^{5}}{a^{20}}$.