Simplify (-3(h^3t^-5)^-3)/(6h^4)

$\frac{- 3 {(h^{3} t^{- 5})}^{- 3}}{6 h^{4}}$

Reduce the expression by cancelling the common factors.

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

$\frac{- 3}{6 h^{4} {(h^{3} t^{- 5})}^{3}}$

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{6 h^{4} {(h^{3} t^{- 5})}^{3}}$

Cancel the common factors.

Factor $3$ out of $6 h^{4} {(h^{3} t^{- 5})}^{3}$ .

$\frac{3 (- 1)}{3 (2 h^{4} {(h^{3} t^{- 5})}^{3})}$

Cancel the common factor.

$\frac{3 \cdot - 1}{3 (2 h^{4} {(h^{3} t^{- 5})}^{3})}$

Rewrite the expression.

$\frac{- 1}{2 h^{4} {(h^{3} t^{- 5})}^{3}}$

Simplify the denominator.

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

$\frac{- 1}{2 h^{4} {(h^{3})}^{3} {(t^{- 5})}^{3}}$

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

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

$\frac{- 1}{2 h^{4} h^{3 \cdot 3} {(t^{- 5})}^{3}}$

Multiply $3$ by $3$ .

$\frac{- 1}{2 h^{4} h^{9} {(t^{- 5})}^{3}}$

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

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

$\frac{- 1}{2 h^{4} h^{9} t^{- 5 \cdot 3}}$

Multiply $- 5$ by $3$ .

$\frac{- 1}{2 h^{4} h^{9} t^{- 15}}$

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

$\frac{- 1}{2 h^{4} h^{9} \frac{1}{t^{15}}}$

Combine exponents.

Multiply $h^{4}$ by $h^{9}$ by adding the exponents.

Move $h^{9}$ .

$\frac{- 1}{2 (h^{9} h^{4}) \frac{1}{t^{15}}}$

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

$\frac{- 1}{2 h^{9 + 4} \frac{1}{t^{15}}}$

Add $9$ and $4$ .

$\frac{- 1}{2 h^{13} \frac{1}{t^{15}}}$

Combine $2$ and $\frac{1}{t^{15}}$ .

$\frac{- 1}{h^{13} \frac{2}{t^{15}}}$

Combine $h^{13}$ and $\frac{2}{t^{15}}$ .

$\frac{- 1}{\frac{h^{13} \cdot 2}{t^{15}}}$

Move $2$ to the left of $h^{13}$ .

$\frac{- 1}{\frac{2 h^{13}}{t^{15}}}$

Multiply the numerator by the reciprocal of the denominator.

$- \frac{t^{15}}{2 h^{13}}$