Write the Fraction in Simplest Form (4z^-1)/(-3(z^5)^3)

$\frac{4 z^{- 1}}{- 3 {(z^{5})}^{3}}$

Move $z^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{- 3 {(z^{5})}^{3} z}$

Simplify the denominator.

Multiply the exponents in ${(z^{5})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4}{- 3 z^{5 \cdot 3} z}$

Multiply $5$ by $3$ .

$\frac{4}{- 3 z^{15} z}$

Combine exponents.

Raise $z$ to the power of $1$ .

$\frac{4}{- 3 (z^{1} z^{15})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{- 3 z^{1 + 15}}$

Add $1$ and $15$ .

$\frac{4}{- 3 z^{16}}$

Move the negative in front of the fraction.

$- \frac{4}{3 z^{16}}$