Simplify (x^3y^4z^5)^(4/5)

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

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

Apply the product rule to $x^{3} y^{4} z^{5}$ .

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

Apply the product rule to $x^{3} y^{4}$ .

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

Multiply the exponents in ${(x^{3})}^{\frac{4}{5}}$ .

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

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

Multiply $3 (\frac{4}{5})$ .

Combine $3$ and $\frac{4}{5}$ .

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

Multiply $3$ by $4$ .

$x^{\frac{12}{5}} {(y^{4})}^{\frac{4}{5}} {(z^{5})}^{\frac{4}{5}}$

Multiply the exponents in ${(y^{4})}^{\frac{4}{5}}$ .

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

$x^{\frac{12}{5}} y^{4 (\frac{4}{5})} {(z^{5})}^{\frac{4}{5}}$

Multiply $4 (\frac{4}{5})$ .

Combine $4$ and $\frac{4}{5}$ .

$x^{\frac{12}{5}} y^{\frac{4 \cdot 4}{5}} {(z^{5})}^{\frac{4}{5}}$

Multiply $4$ by $4$ .

$x^{\frac{12}{5}} y^{\frac{16}{5}} {(z^{5})}^{\frac{4}{5}}$

Multiply the exponents in ${(z^{5})}^{\frac{4}{5}}$ .

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

$x^{\frac{12}{5}} y^{\frac{16}{5}} z^{5 (\frac{4}{5})}$

Cancel the common factor of $5$ .

Cancel the common factor.

$x^{\frac{12}{5}} y^{\frac{16}{5}} z^{5 (\frac{4}{5})}$

Rewrite the expression.

$x^{\frac{12}{5}} y^{\frac{16}{5}} z^{4}$

Reorder factors in $x^{\frac{12}{5}} y^{\frac{16}{5}} z^{4}$ .

$z^{4} x^{\frac{12}{5}} y^{\frac{16}{5}}$