Simplify (x^12y^0z^9)^(1/3)

${(x^{12} y^{0} z^{9})}^{\frac{1}{3}}$

Step 1

Anything raised to $0$ is $1$ .

${(x^{12} \cdot 1 z^{9})}^{\frac{1}{3}}$

Step 2

Multiply $x^{12}$ by $1$ .

${(x^{12} z^{9})}^{\frac{1}{3}}$

Step 3

Apply the product rule to $x^{12} z^{9}$ .

${(x^{12})}^{\frac{1}{3}} {(z^{9})}^{\frac{1}{3}}$

Step 4

Multiply the exponents in ${(x^{12})}^{\frac{1}{3}}$ .

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

$x^{12 (\frac{1}{3})} {(z^{9})}^{\frac{1}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$x^{3 (4) \frac{1}{3}} {(z^{9})}^{\frac{1}{3}}$

Cancel the common factor.

$x^{3 \cdot 4 \frac{1}{3}} {(z^{9})}^{\frac{1}{3}}$

Rewrite the expression.

$x^{4} {(z^{9})}^{\frac{1}{3}}$

Step 5

Multiply the exponents in ${(z^{9})}^{\frac{1}{3}}$ .

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

$x^{4} z^{9 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$x^{4} z^{3 (3) \frac{1}{3}}$

Cancel the common factor.

$x^{4} z^{3 \cdot 3 \frac{1}{3}}$

Rewrite the expression.

$x^{4} z^{3}$