Simplify (5^(1/3)*7^(1/4))^3

${(5^{\frac{1}{3}} \cdot 7^{\frac{1}{4}})}^{3}$

Apply the product rule to $5^{\frac{1}{3}} \cdot 7^{\frac{1}{4}}$ .

${(5^{\frac{1}{3}})}^{3} \cdot {(7^{\frac{1}{4}})}^{3}$

Multiply the exponents in ${(5^{\frac{1}{3}})}^{3}$ .

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

$5^{\frac{1}{3} \cdot 3} \cdot {(7^{\frac{1}{4}})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{\frac{1}{3} \cdot 3} \cdot {(7^{\frac{1}{4}})}^{3}$

Rewrite the expression.

$5^{1} \cdot {(7^{\frac{1}{4}})}^{3}$

Evaluate the exponent.

$5 \cdot {(7^{\frac{1}{4}})}^{3}$

Multiply the exponents in ${(7^{\frac{1}{4}})}^{3}$ .

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

$5 \cdot 7^{\frac{1}{4} \cdot 3}$

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

$5 \cdot 7^{\frac{3}{4}}$

The result can be shown in multiple forms.

Exact Form:

$5 \cdot 7^{\frac{3}{4}}$

Decimal Form:

$21.51758535 \dots$