Write the Fraction in Simplest Form (4b^-8)/((-3b^5)^5)

$\frac{4 b^{- 8}}{{(- 3 b^{5})}^{5}}$

Move $b^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{{(- 3 b^{5})}^{5} b^{8}}$

Simplify the denominator.

Apply the product rule to $- 3 b^{5}$ .

$\frac{4}{{(- 3)}^{5} {(b^{5})}^{5} b^{8}}$

Raise $- 3$ to the power of $5$ .

$\frac{4}{- 243 {(b^{5})}^{5} b^{8}}$

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

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

$\frac{4}{- 243 b^{5 \cdot 5} b^{8}}$

Multiply $5$ by $5$ .

$\frac{4}{- 243 b^{25} b^{8}}$

Multiply $b^{25}$ by $b^{8}$ by adding the exponents.

Move $b^{8}$ .

$\frac{4}{- 243 (b^{8} b^{25})}$

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

$\frac{4}{- 243 b^{8 + 25}}$

Add $8$ and $25$ .

$\frac{4}{- 243 b^{33}}$

Move the negative in front of the fraction.

$- \frac{4}{243 b^{33}}$