Evaluate (3(2a)^(3/2))^2

${(3 {(2 a)}^{\frac{3}{2}})}^{2}$

Apply the product rule to $2 a$ .

${(3 (2^{\frac{3}{2}} a^{\frac{3}{2}}))}^{2}$

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

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

${(3 \cdot 2^{\frac{3}{2}})}^{2} {(a^{\frac{3}{2}})}^{2}$

Apply the product rule to $3 \cdot 2^{\frac{3}{2}}$ .

$3^{2} \cdot {(2^{\frac{3}{2}})}^{2} {(a^{\frac{3}{2}})}^{2}$

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

$9 \cdot {(2^{\frac{3}{2}})}^{2} {(a^{\frac{3}{2}})}^{2}$

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

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

$9 \cdot 2^{\frac{3}{2} \cdot 2} {(a^{\frac{3}{2}})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 \cdot 2^{\frac{3}{2} \cdot 2} {(a^{\frac{3}{2}})}^{2}$

Rewrite the expression.

$9 \cdot 2^{3} {(a^{\frac{3}{2}})}^{2}$

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

$9 \cdot 8 {(a^{\frac{3}{2}})}^{2}$

Multiply $9$ by $8$ .

$72 {(a^{\frac{3}{2}})}^{2}$

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

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

$72 a^{\frac{3}{2} \cdot 2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$72 a^{\frac{3}{2} \cdot 2}$

Rewrite the expression.

$72 a^{3}$