Simplify (3x^10c^10)/(-4(x^3c^2)^-4)

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

Step 1

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

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

Step 2

Simplify the numerator.

Apply the product rule to $x^{3} c^{2}$ .

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

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

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

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

Multiply $3$ by $4$ .

$\frac{3 x^{10} c^{10} x^{12} {(c^{2})}^{4}}{- 4}$

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

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

$\frac{3 x^{10} c^{10} x^{12} c^{2 \cdot 4}}{- 4}$

Multiply $2$ by $4$ .

$\frac{3 x^{10} c^{10} x^{12} c^{8}}{- 4}$

Combine exponents.

Multiply $x^{10}$ by $x^{12}$ by adding the exponents.

Move $x^{12}$ .

$\frac{3 (x^{12} x^{10}) c^{10} c^{8}}{- 4}$

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

$\frac{3 x^{12 + 10} c^{10} c^{8}}{- 4}$

Add $12$ and $10$ .

$\frac{3 x^{22} c^{10} c^{8}}{- 4}$

Multiply $c^{10}$ by $c^{8}$ by adding the exponents.

Move $c^{8}$ .

$\frac{3 x^{22} (c^{8} c^{10})}{- 4}$

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

$\frac{3 x^{22} c^{8 + 10}}{- 4}$

Add $8$ and $10$ .

$\frac{3 x^{22} c^{18}}{- 4}$

Step 3

Move the negative in front of the fraction.

$- \frac{3 x^{22} c^{18}}{4}$