Simplify (2a^(3/2))^(1/2)

${(2 a^{\frac{3}{2}})}^{\frac{1}{2}}$

Step 1

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

$2^{\frac{1}{2}} {(a^{\frac{3}{2}})}^{\frac{1}{2}}$

Step 2

Multiply the exponents in ${(a^{\frac{3}{2}})}^{\frac{1}{2}}$ .

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

$2^{\frac{1}{2}} a^{\frac{3}{2} \cdot \frac{1}{2}}$

Multiply $\frac{3}{2} \cdot \frac{1}{2}$ .

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

$2^{\frac{1}{2}} a^{\frac{3}{2 \cdot 2}}$

Multiply $2$ by $2$ .

$2^{\frac{1}{2}} a^{\frac{3}{4}}$