Simplify (3m^(1/4)n^(2/3))^3

${(3 m^{\frac{1}{4}} n^{\frac{2}{3}})}^{3}$

Step 1

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

Apply the product rule to $3 m^{\frac{1}{4}} n^{\frac{2}{3}}$ .

${(3 m^{\frac{1}{4}})}^{3} {(n^{\frac{2}{3}})}^{3}$

Apply the product rule to $3 m^{\frac{1}{4}}$ .

$3^{3} {(m^{\frac{1}{4}})}^{3} {(n^{\frac{2}{3}})}^{3}$

Step 2

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

$27 {(m^{\frac{1}{4}})}^{3} {(n^{\frac{2}{3}})}^{3}$

Step 3

Multiply the exponents in ${(m^{\frac{1}{4}})}^{3}$ .

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

$27 m^{\frac{1}{4} \cdot 3} {(n^{\frac{2}{3}})}^{3}$

Combine $\frac{1}{4}$ and $3$ .

$27 m^{\frac{3}{4}} {(n^{\frac{2}{3}})}^{3}$

Step 4

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

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

$27 m^{\frac{3}{4}} n^{\frac{2}{3} \cdot 3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$27 m^{\frac{3}{4}} n^{\frac{2}{3} \cdot 3}$

Rewrite the expression.

$27 m^{\frac{3}{4}} n^{2}$

Step 5

Reorder factors in $27 m^{\frac{3}{4}} n^{2}$ .

$27 n^{2} m^{\frac{3}{4}}$