Calculate the Result of the Fractions and Powers: 1/(-3)·3^(-4)·5^3

Apply the laws of exponents for negative exponents, in the opposite direction:

$\frac{1}{a^n} = a^{-n}$

Thus we can handle the leftmost term in the multiplication:

$\frac{1}{-3}\cdot3^{-4}\cdot5^3=-\frac{1}{3}\cdot3^{-4}\cdot5^3=-3^{-1}\cdot3^{-4}\cdot5^3$ In the first step we simplified the first fraction whilst remembering that dividing a positive number by a negative number gives a negative result. In the second step we applied the aforementioned law of exponents,

Before we continue, let's note and emphasize that the minus sign is not under the exponent in the first term of the multiplication, meaning - the exponent doesn't apply to it but only to the number 3.

Next, we'll recall the law of exponents for multiplication of terms with identical bases:

$a^m\cdot a^n=a^{m+n}$and we'll apply this law to the last expression we got:

$-3^{-1}\cdot3^{-4}\cdot5^3=-3^{-1+(-4)}\cdot5^3=-3^{-1-4}\cdot5^3=-3^{-5}\cdot5^3$when we applied the aforementioned law of exponents only to the terms with identical bases and carried the minus sign throughout the calculation for the reason we mentioned earlier,

Let's summarize the steps so far:

$\frac{1}{-3}\cdot3^{-4}\cdot5^3=-3^{-1}\cdot3^{-4}\cdot5^3 =-3^{-1-4}\cdot5^3=-3^{-5}\cdot5^3$

Note that this answer isn't among the answer choices, however, we can apply the negative exponent law once again:

$a^{-n}=\frac{1}{a^n}$We'll apply it to the first term in the multiplication of terms that we obtained in the last step:

$-3^{-5}\cdot5^3=-\frac{1}{3^5}\cdot5^3=-\frac{5^3}{3^5}$In the first step we applied the aforementioned law to the first term in the multiplication, and in the next step we performed the fraction multiplication whilst remembering that multiplying by a fraction is essentially multiplying by the numerator,

Let's summarize the solution steps again:
$\frac{1}{-3}\cdot3^{-4}\cdot5^3=-3^{-1}\cdot3^{-4}\cdot5^3 =-3^{-5}\cdot5^3 =-\frac{5^3}{3^5}$

Therefore, the correct answer is answer B.