Simplify ((a^2b^4c)^2(6a^3b)(2c^5)^3)/(4a^6b^12c^3)

$\frac{{(a^{2} b^{4} c)}^{2} (6 a^{3} b) {(2 c^{5})}^{3}}{4 a^{6} b^{12} c^{3}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of ${(a^{2} b^{4} c)}^{2} (6 a^{3} b) {(2 c^{5})}^{3}$ .

$\frac{2 ({(a^{2} b^{4} c)}^{2} (3 a^{3} b) {(2 c^{5})}^{3})}{4 a^{6} b^{12} c^{3}}$

Cancel the common factors.

Factor $2$ out of $4 a^{6} b^{12} c^{3}$ .

$\frac{2 ({(a^{2} b^{4} c)}^{2} (3 a^{3} b) {(2 c^{5})}^{3})}{2 (2 a^{6} b^{12} c^{3})}$

Cancel the common factor.

$\frac{2 ({(a^{2} b^{4} c)}^{2} (3 a^{3} b) {(2 c^{5})}^{3})}{2 (2 a^{6} b^{12} c^{3})}$

Rewrite the expression.

$\frac{{(a^{2} b^{4} c)}^{2} (3 a^{3} b) {(2 c^{5})}^{3}}{2 a^{6} b^{12} c^{3}}$

Cancel the common factor of $a^{3}$ and $a^{6}$ .

Factor $a^{3}$ out of ${(a^{2} b^{4} c)}^{2} (3 a^{3} b) {(2 c^{5})}^{3}$ .

$\frac{a^{3} ({(a^{2} b^{4} c)}^{2} (3 b) {(2 c^{5})}^{3})}{2 a^{6} b^{12} c^{3}}$

Cancel the common factors.

Factor $a^{3}$ out of $2 a^{6} b^{12} c^{3}$ .

$\frac{a^{3} ({(a^{2} b^{4} c)}^{2} (3 b) {(2 c^{5})}^{3})}{a^{3} (2 a^{3} b^{12} c^{3})}$

Cancel the common factor.

$\frac{a^{3} ({(a^{2} b^{4} c)}^{2} (3 b) {(2 c^{5})}^{3})}{a^{3} (2 a^{3} b^{12} c^{3})}$

Rewrite the expression.

$\frac{{(a^{2} b^{4} c)}^{2} (3 b) {(2 c^{5})}^{3}}{2 a^{3} b^{12} c^{3}}$

Cancel the common factor of $b$ and $b^{12}$ .

Factor $b$ out of ${(a^{2} b^{4} c)}^{2} (3 b) {(2 c^{5})}^{3}$ .

$\frac{b ({(a^{2} b^{4} c)}^{2} \cdot (3) {(2 c^{5})}^{3})}{2 a^{3} b^{12} c^{3}}$

Cancel the common factors.

Factor $b$ out of $2 a^{3} b^{12} c^{3}$ .

$\frac{b ({(a^{2} b^{4} c)}^{2} \cdot (3) {(2 c^{5})}^{3})}{b (2 a^{3} b^{11} c^{3})}$

Cancel the common factor.

$\frac{b ({(a^{2} b^{4} c)}^{2} \cdot (3) {(2 c^{5})}^{3})}{b (2 a^{3} b^{11} c^{3})}$

Rewrite the expression.

$\frac{{(a^{2} b^{4} c)}^{2} \cdot (3) {(2 c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

Simplify the numerator.

Apply the product rule to $a^{2} b^{4} c$ .

$\frac{{(a^{2} b^{4})}^{2} c^{2} \cdot 3 {(2 c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

Apply the product rule to $2 c^{5}$ .

$\frac{{(a^{2} b^{4})}^{2} c^{2} \cdot 3 \cdot 2^{3} {(c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

Apply the product rule to $a^{2} b^{4}$ .

$\frac{{(a^{2})}^{2} {(b^{4})}^{2} c^{2} \cdot 3 \cdot 2^{3} {(c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

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

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

$\frac{a^{2 \cdot 2} {(b^{4})}^{2} c^{2} \cdot 3 \cdot 2^{3} {(c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

Multiply $2$ by $2$ .

$\frac{a^{4} {(b^{4})}^{2} c^{2} \cdot 3 \cdot 2^{3} {(c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

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

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

$\frac{a^{4} b^{4 \cdot 2} c^{2} \cdot 3 \cdot 2^{3} {(c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

Multiply $4$ by $2$ .

$\frac{a^{4} b^{8} c^{2} \cdot 3 \cdot 2^{3} {(c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

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

$\frac{a^{4} b^{8} c^{2} \cdot 3 \cdot 8 {(c^{5})}^{3}}{2 a^{3} b^{11} c^{3}}$

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

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

$\frac{a^{4} b^{8} c^{2} \cdot 3 \cdot 8 c^{5 \cdot 3}}{2 a^{3} b^{11} c^{3}}$

Multiply $5$ by $3$ .

$\frac{a^{4} b^{8} c^{2} \cdot 3 \cdot 8 c^{15}}{2 a^{3} b^{11} c^{3}}$

Combine exponents.

Multiply $8$ by $3$ .

$\frac{a^{4} b^{8} c^{2} \cdot 24 c^{15}}{2 a^{3} b^{11} c^{3}}$

Multiply $c^{2}$ by $c^{15}$ by adding the exponents.

Move $c^{15}$ .

$\frac{a^{4} b^{8} (c^{15} c^{2}) \cdot 24}{2 a^{3} b^{11} c^{3}}$

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

$\frac{a^{4} b^{8} c^{15 + 2} \cdot 24}{2 a^{3} b^{11} c^{3}}$

Add $15$ and $2$ .

$\frac{a^{4} b^{8} c^{17} \cdot 24}{2 a^{3} b^{11} c^{3}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $a^{4}$ and $a^{3}$ .

Factor $a^{3}$ out of $a^{4} b^{8} c^{17} \cdot 24$ .

$\frac{a^{3} (a b^{8} c^{17} \cdot 24)}{2 a^{3} b^{11} c^{3}}$

Cancel the common factors.

Factor $a^{3}$ out of $2 a^{3} b^{11} c^{3}$ .

$\frac{a^{3} (a b^{8} c^{17} \cdot 24)}{a^{3} (2 b^{11} c^{3})}$

Cancel the common factor.

$\frac{a^{3} (a b^{8} c^{17} \cdot 24)}{a^{3} (2 b^{11} c^{3})}$

Rewrite the expression.

$\frac{a b^{8} c^{17} \cdot 24}{2 b^{11} c^{3}}$

Cancel the common factor of $b^{8}$ and $b^{11}$ .

Factor $b^{8}$ out of $a b^{8} c^{17} \cdot 24$ .

$\frac{b^{8} (a c^{17} \cdot 24)}{2 b^{11} c^{3}}$

Cancel the common factors.

Factor $b^{8}$ out of $2 b^{11} c^{3}$ .

$\frac{b^{8} (a c^{17} \cdot 24)}{b^{8} (2 b^{3} c^{3})}$

Cancel the common factor.

$\frac{b^{8} (a c^{17} \cdot 24)}{b^{8} (2 b^{3} c^{3})}$

Rewrite the expression.

$\frac{a c^{17} \cdot 24}{2 b^{3} c^{3}}$

Cancel the common factor of $c^{17}$ and $c^{3}$ .

Factor $c^{3}$ out of $a c^{17} \cdot 24$ .

$\frac{c^{3} (a c^{14} \cdot 24)}{2 b^{3} c^{3}}$

Cancel the common factors.

Factor $c^{3}$ out of $2 b^{3} c^{3}$ .

$\frac{c^{3} (a c^{14} \cdot 24)}{c^{3} (2 b^{3})}$

Cancel the common factor.

$\frac{c^{3} (a c^{14} \cdot 24)}{c^{3} (2 b^{3})}$

Rewrite the expression.

$\frac{a c^{14} \cdot 24}{2 b^{3}}$

Cancel the common factor of $24$ and $2$ .

Factor $2$ out of $a c^{14} \cdot 24$ .

$\frac{2 (a c^{14} \cdot 12)}{2 b^{3}}$

Cancel the common factors.

Factor $2$ out of $2 b^{3}$ .

$\frac{2 (a c^{14} \cdot 12)}{2 (b^{3})}$

Cancel the common factor.

$\frac{2 (a c^{14} \cdot 12)}{2 b^{3}}$

Rewrite the expression.

$\frac{a c^{14} \cdot 12}{b^{3}}$

Move $12$ to the left of $a c^{14}$ .

$\frac{12 a c^{14}}{b^{3}}$

Simplify ((a^2b^4c)^2(6a^3b)(2c^5)^3)/(4a^6b^12c^3)

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