Simplify ((3t^-4n^-5)^-3)/(4n^3)

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

Move ${(3 t^{- 4} n^{- 5})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Simplify the denominator.

Apply the product rule to $3 t^{- 4} n^{- 5}$ .

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

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

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

Combine $3$ and $\frac{1}{t^{4}}$ .

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

Apply the product rule to $\frac{3}{t^{4}}$ .

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

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

$\frac{1}{4 n^{3} \frac{27}{{(t^{4})}^{3}} {(n^{- 5})}^{3}}$

Multiply the exponents in ${(t^{4})}^{3}$ .

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

$\frac{1}{4 n^{3} \frac{27}{t^{4 \cdot 3}} {(n^{- 5})}^{3}}$

Multiply $4$ by $3$ .

$\frac{1}{4 n^{3} \frac{27}{t^{12}} {(n^{- 5})}^{3}}$

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

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

$\frac{1}{4 n^{3} \frac{27}{t^{12}} n^{- 5 \cdot 3}}$

Multiply $- 5$ by $3$ .

$\frac{1}{4 n^{3} \frac{27}{t^{12}} n^{- 15}}$

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

$\frac{1}{4 n^{3} \frac{27}{t^{12}} \frac{1}{n^{15}}}$

Combine exponents.

Combine $4$ and $\frac{27}{t^{12}}$ .

$\frac{1}{n^{3} \frac{4 \cdot 27}{t^{12}} \frac{1}{n^{15}}}$

Multiply $4$ by $27$ .

$\frac{1}{n^{3} \frac{108}{t^{12}} \frac{1}{n^{15}}}$

Combine $n^{3}$ and $\frac{108}{t^{12}}$ .

$\frac{1}{\frac{n^{3} \cdot 108}{t^{12}} \cdot \frac{1}{n^{15}}}$

Multiply $\frac{n^{3} \cdot 108}{t^{12}}$ by $\frac{1}{n^{15}}$ .

$\frac{1}{\frac{n^{3} \cdot 108}{t^{12} n^{15}}}$

Reduce the expression $\frac{n^{3} \cdot 108}{t^{12} n^{15}}$ by cancelling the common factors.

Factor $n^{3}$ out of $n^{3} \cdot 108$ .

$\frac{1}{\frac{n^{3} (108)}{t^{12} n^{15}}}$

Factor $n^{3}$ out of $t^{12} n^{15}$ .

$\frac{1}{\frac{n^{3} (108)}{n^{3} (t^{12} n^{12})}}$

Cancel the common factor.

$\frac{1}{\frac{n^{3} \cdot 108}{n^{3} (t^{12} n^{12})}}$

Rewrite the expression.

$\frac{1}{\frac{108}{t^{12} n^{12}}}$

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{t^{12} n^{12}}{108}$

Multiply $\frac{t^{12} n^{12}}{108}$ by $1$ .

$\frac{t^{12} n^{12}}{108}$

Simplify ((3t^-4n^-5)^-3)/(4n^3)

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