Write the Fraction in Simplest Form (3x^9)/((5x^-4)^2)

$\frac{3 x^{9}}{{(5 x^{- 4})}^{2}}$

Simplify the denominator.

Apply the product rule to $5 x^{- 4}$ .

$\frac{3 x^{9}}{5^{2} {(x^{- 4})}^{2}}$

Raise $5$ to the power of $2$ .

$\frac{3 x^{9}}{25 {(x^{- 4})}^{2}}$

Multiply the exponents in ${(x^{- 4})}^{2}$ .

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

$\frac{3 x^{9}}{25 x^{- 4 \cdot 2}}$

Multiply $- 4$ by $2$ .

$\frac{3 x^{9}}{25 x^{- 8}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 x^{9}}{25 \frac{1}{x^{8}}}$

Combine $25$ and $\frac{1}{x^{8}}$ .

$\frac{3 x^{9}}{\frac{25}{x^{8}}}$

Multiply the numerator by the reciprocal of the denominator.

$3 x^{9} \frac{x^{8}}{25}$

Multiply $3 x^{9} \frac{x^{8}}{25}$ .

Combine $3$ and $\frac{x^{8}}{25}$ .

$x^{9} \frac{3 x^{8}}{25}$

Combine $x^{9}$ and $\frac{3 x^{8}}{25}$ .

$\frac{x^{9} (3 x^{8})}{25}$

Multiply $x^{9}$ by $x^{8}$ by adding the exponents.

Move $x^{8}$ .

$\frac{x^{8} x^{9} \cdot 3}{25}$

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

$\frac{x^{8 + 9} \cdot 3}{25}$

Add $8$ and $9$ .

$\frac{x^{17} \cdot 3}{25}$

Move $3$ to the left of $x^{17}$ .

$\frac{3 x^{17}}{25}$