Simplify ((2y^-5n^4)^-3)/(6y^7n^-5)

$\frac{{(2 y^{- 5} n^{4})}^{- 3}}{6 y^{7} n^{- 5}}$

Simplify the expression.

Move ${(2 y^{- 5} n^{4})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{6 y^{7} n^{- 5} {(2 y^{- 5} n^{4})}^{3}}$

Move $n^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{n^{5}}{6 y^{7} {(2 y^{- 5} n^{4})}^{3}}$

Simplify the denominator.

Apply the product rule to $2 y^{- 5} n^{4}$ .

$\frac{n^{5}}{6 y^{7} {(2 y^{- 5})}^{3} {(n^{4})}^{3}}$

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

$\frac{n^{5}}{6 y^{7} {(2 \frac{1}{y^{5}})}^{3} {(n^{4})}^{3}}$

Combine $2$ and $\frac{1}{y^{5}}$ .

$\frac{n^{5}}{6 y^{7} {(\frac{2}{y^{5}})}^{3} {(n^{4})}^{3}}$

Apply the product rule to $\frac{2}{y^{5}}$ .

$\frac{n^{5}}{6 y^{7} \frac{2^{3}}{{(y^{5})}^{3}} {(n^{4})}^{3}}$

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

$\frac{n^{5}}{6 y^{7} \frac{8}{{(y^{5})}^{3}} {(n^{4})}^{3}}$

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

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

$\frac{n^{5}}{6 y^{7} \frac{8}{y^{5 \cdot 3}} {(n^{4})}^{3}}$

Multiply $5$ by $3$ .

$\frac{n^{5}}{6 y^{7} \frac{8}{y^{15}} {(n^{4})}^{3}}$

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

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

$\frac{n^{5}}{6 y^{7} \frac{8}{y^{15}} n^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{n^{5}}{6 y^{7} \frac{8}{y^{15}} n^{12}}$

Combine exponents.

Combine $6$ and $\frac{8}{y^{15}}$ .

$\frac{n^{5}}{y^{7} \frac{6 \cdot 8}{y^{15}} n^{12}}$

Multiply $6$ by $8$ .

$\frac{n^{5}}{y^{7} \frac{48}{y^{15}} n^{12}}$

Combine $y^{7}$ and $\frac{48}{y^{15}}$ .

$\frac{n^{5}}{\frac{y^{7} \cdot 48}{y^{15}} n^{12}}$

Combine $\frac{y^{7} \cdot 48}{y^{15}}$ and $n^{12}$ .

$\frac{n^{5}}{\frac{y^{7} \cdot 48 n^{12}}{y^{15}}}$

Reduce the expression $\frac{y^{7} \cdot 48 n^{12}}{y^{15}}$ by cancelling the common factors.

Factor $y^{7}$ out of $y^{7} \cdot 48 n^{12}$ .

$\frac{n^{5}}{\frac{y^{7} (48 n^{12})}{y^{15}}}$

Factor $y^{7}$ out of $y^{15}$ .

$\frac{n^{5}}{\frac{y^{7} (48 n^{12})}{y^{7} y^{8}}}$

Cancel the common factor.

$\frac{n^{5}}{\frac{y^{7} (48 n^{12})}{y^{7} y^{8}}}$

Rewrite the expression.

$\frac{n^{5}}{\frac{48 n^{12}}{y^{8}}}$

Multiply the numerator by the reciprocal of the denominator.

$n^{5} \frac{y^{8}}{48 n^{12}}$

Cancel the common factor of $n^{5}$ .

Factor $n^{5}$ out of $48 n^{12}$ .

$n^{5} \frac{y^{8}}{n^{5} (48 n^{7})}$

Cancel the common factor.

$n^{5} \frac{y^{8}}{n^{5} (48 n^{7})}$

Rewrite the expression.

$\frac{y^{8}}{48 n^{7}}$

Simplify ((2y^-5n^4)^-3)/(6y^7n^-5)

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