Simplify the Radical Expression (2^(12/5)x^2)^(5/3)

${(2^{\frac{12}{5}} x^{2})}^{\frac{5}{3}}$

Step 1

Apply the product rule to $2^{\frac{12}{5}} x^{2}$ .

${(2^{\frac{12}{5}})}^{\frac{5}{3}} {(x^{2})}^{\frac{5}{3}}$

Step 2

Multiply the exponents in ${(2^{\frac{12}{5}})}^{\frac{5}{3}}$ .

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

$2^{\frac{12}{5} \cdot \frac{5}{3}} {(x^{2})}^{\frac{5}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$2^{\frac{3 (4)}{5} \cdot \frac{5}{3}} {(x^{2})}^{\frac{5}{3}}$

Cancel the common factor.

$2^{\frac{3 \cdot 4}{5} \cdot \frac{5}{3}} {(x^{2})}^{\frac{5}{3}}$

Rewrite the expression.

$2^{\frac{4}{5} \cdot 5} {(x^{2})}^{\frac{5}{3}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$2^{\frac{4}{5} \cdot 5} {(x^{2})}^{\frac{5}{3}}$

Rewrite the expression.

$2^{4} {(x^{2})}^{\frac{5}{3}}$

Step 3

Raise $2$ to the power of $4$ .

$16 {(x^{2})}^{\frac{5}{3}}$

Step 4

Multiply the exponents in ${(x^{2})}^{\frac{5}{3}}$ .

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

$16 x^{2 (\frac{5}{3})}$

Multiply $2 (\frac{5}{3})$ .

Combine $2$ and $\frac{5}{3}$ .

$16 x^{\frac{2 \cdot 5}{3}}$

Multiply $2$ by $5$ .

$16 x^{\frac{10}{3}}$