Simplify ((-3s^-1c^-4)^2)/(4s^10c^-10)

$\frac{{(- 3 s^{- 1} c^{- 4})}^{2}}{4 s^{10} c^{- 10}}$

Move $c^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(- 3 s^{- 1} c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Simplify the numerator.

Apply the product rule to $- 3 s^{- 1} c^{- 4}$ .

$\frac{{(- 3 s^{- 1})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

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

$\frac{{(- 3 \frac{1}{s})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Combine $- 3$ and $\frac{1}{s}$ .

$\frac{{(\frac{- 3}{s})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Move the negative in front of the fraction.

$\frac{{(- \frac{3}{s})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{3}{s}$ .

$\frac{{(- 1)}^{2} {(\frac{3}{s})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

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

$\frac{{(- 1)}^{2} \frac{3^{2}}{s^{2}} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Raise $- 1$ to the power of $2$ .

$\frac{1 \frac{3^{2}}{s^{2}} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Multiply $\frac{3^{2}}{s^{2}}$ by $1$ .

$\frac{\frac{3^{2}}{s^{2}} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

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

$\frac{\frac{9}{s^{2}} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

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

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

$\frac{\frac{9}{s^{2}} c^{- 4 \cdot 2} c^{10}}{4 s^{10}}$

Multiply $- 4$ by $2$ .

$\frac{\frac{9}{s^{2}} c^{- 8} c^{10}}{4 s^{10}}$

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

$\frac{\frac{9}{s^{2}} \cdot \frac{1}{c^{8}} c^{10}}{4 s^{10}}$

Combine exponents.

Multiply $\frac{9}{s^{2}}$ by $\frac{1}{c^{8}}$ .

$\frac{\frac{9}{s^{2} c^{8}} c^{10}}{4 s^{10}}$

Combine $\frac{9}{s^{2} c^{8}}$ and $c^{10}$ .

$\frac{\frac{9 c^{10}}{s^{2} c^{8}}}{4 s^{10}}$

Reduce the expression $\frac{9 c^{10}}{s^{2} c^{8}}$ by cancelling the common factors.

Factor $c^{8}$ out of $9 c^{10}$ .

$\frac{\frac{c^{8} (9 c^{2})}{s^{2} c^{8}}}{4 s^{10}}$

Factor $c^{8}$ out of $s^{2} c^{8}$ .

$\frac{\frac{c^{8} (9 c^{2})}{c^{8} s^{2}}}{4 s^{10}}$

Cancel the common factor.

$\frac{\frac{c^{8} (9 c^{2})}{c^{8} s^{2}}}{4 s^{10}}$

Rewrite the expression.

$\frac{\frac{9 c^{2}}{s^{2}}}{4 s^{10}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{9 c^{2}}{s^{2}} \cdot \frac{1}{4 s^{10}}$

Combine.

$\frac{9 c^{2} \cdot 1}{s^{2} (4 s^{10})}$

Multiply $s^{2}$ by $s^{10}$ by adding the exponents.

Move $s^{10}$ .

$\frac{9 c^{2} \cdot 1}{s^{10} s^{2} \cdot 4}$

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

$\frac{9 c^{2} \cdot 1}{s^{10 + 2} \cdot 4}$

Add $10$ and $2$ .

$\frac{9 c^{2} \cdot 1}{s^{12} \cdot 4}$

Multiply $9 c^{2}$ by $1$ .

$\frac{9 c^{2}}{s^{12} \cdot 4}$

Move $4$ to the left of $s^{12}$ .

$\frac{9 c^{2}}{4 s^{12}}$

Simplify ((-3s^-1c^-4)^2)/(4s^10c^-10)

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