Simplify (3a^2bc^3)^3

${(3 a^{2} b c^{3})}^{3}$

Step 1

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

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

${(3 a^{2} b)}^{3} {(c^{3})}^{3}$

Apply the product rule to $3 a^{2} b$ .

${(3 a^{2})}^{3} b^{3} {(c^{3})}^{3}$

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

$3^{3} {(a^{2})}^{3} b^{3} {(c^{3})}^{3}$

Step 2

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

$27 {(a^{2})}^{3} b^{3} {(c^{3})}^{3}$

Step 3

Multiply the exponents in ${(a^{2})}^{3}$ .

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

$27 a^{2 \cdot 3} b^{3} {(c^{3})}^{3}$

Multiply $2$ by $3$ .

$27 a^{6} b^{3} {(c^{3})}^{3}$

Step 4

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

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

$27 a^{6} b^{3} c^{3 \cdot 3}$

Multiply $3$ by $3$ .

$27 a^{6} b^{3} c^{9}$