Simplify (6n^-5)(3n^-3)^2

$(6 n^{- 5}) {(3 n^{- 3})}^{2}$

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

$6 \frac{1}{n^{5}} {(3 n^{- 3})}^{2}$

Combine $6$ and $\frac{1}{n^{5}}$ .

$\frac{6}{n^{5}} {(3 n^{- 3})}^{2}$

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

$\frac{6}{n^{5}} {(3 \frac{1}{n^{3}})}^{2}$

Combine $3$ and $\frac{1}{n^{3}}$ .

$\frac{6}{n^{5}} {(\frac{3}{n^{3}})}^{2}$

Apply the product rule to $\frac{3}{n^{3}}$ .

$\frac{6}{n^{5}} \cdot \frac{3^{2}}{{(n^{3})}^{2}}$

Combine.

$\frac{6 \cdot 3^{2}}{n^{5} {(n^{3})}^{2}}$

Simplify the expression.

Raise $3$ to the power of $2$ .

$\frac{6 \cdot 9}{n^{5} {(n^{3})}^{2}}$

Multiply the exponents in ${(n^{3})}^{2}$ .

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

$\frac{6 \cdot 9}{n^{5} n^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{6 \cdot 9}{n^{5} n^{6}}$

Multiply $6$ by $9$ .

$\frac{54}{n^{5} n^{6}}$

Multiply $n^{5}$ by $n^{6}$ by adding the exponents.

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

$\frac{54}{n^{5 + 6}}$

Add $5$ and $6$ .

$\frac{54}{n^{11}}$