Simplify (128c^15d^11e^5)^(1/3)

${(128 c^{15} d^{11} e^{5})}^{\frac{1}{3}}$

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

Apply the product rule to $128 c^{15} d^{11} e^{5}$ .

${(128 c^{15} d^{11})}^{\frac{1}{3}} {(e^{5})}^{\frac{1}{3}}$

Apply the product rule to $128 c^{15} d^{11}$ .

${(128 c^{15})}^{\frac{1}{3}} {(d^{11})}^{\frac{1}{3}} {(e^{5})}^{\frac{1}{3}}$

Apply the product rule to $128 c^{15}$ .

$128^{\frac{1}{3}} {(c^{15})}^{\frac{1}{3}} {(d^{11})}^{\frac{1}{3}} {(e^{5})}^{\frac{1}{3}}$

Multiply the exponents in ${(c^{15})}^{\frac{1}{3}}$ .

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

$128^{\frac{1}{3}} c^{15 (\frac{1}{3})} {(d^{11})}^{\frac{1}{3}} {(e^{5})}^{\frac{1}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$128^{\frac{1}{3}} c^{3 (5) \frac{1}{3}} {(d^{11})}^{\frac{1}{3}} {(e^{5})}^{\frac{1}{3}}$

Cancel the common factor.

$128^{\frac{1}{3}} c^{3 \cdot 5 \frac{1}{3}} {(d^{11})}^{\frac{1}{3}} {(e^{5})}^{\frac{1}{3}}$

Rewrite the expression.

$128^{\frac{1}{3}} c^{5} {(d^{11})}^{\frac{1}{3}} {(e^{5})}^{\frac{1}{3}}$

Multiply the exponents in ${(d^{11})}^{\frac{1}{3}}$ .

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

$128^{\frac{1}{3}} c^{5} d^{11 (\frac{1}{3})} {(e^{5})}^{\frac{1}{3}}$

Combine $11$ and $\frac{1}{3}$ .

$128^{\frac{1}{3}} c^{5} d^{\frac{11}{3}} {(e^{5})}^{\frac{1}{3}}$

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

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

$128^{\frac{1}{3}} c^{5} d^{\frac{11}{3}} e^{5 (\frac{1}{3})}$

Combine $5$ and $\frac{1}{3}$ .

$128^{\frac{1}{3}} c^{5} d^{\frac{11}{3}} e^{\frac{5}{3}}$

Reorder factors in $128^{\frac{1}{3}} c^{5} d^{\frac{11}{3}} e^{\frac{5}{3}}$ .

$c^{5} \cdot 128^{\frac{1}{3}} d^{\frac{11}{3}} e^{\frac{5}{3}}$