What is (27\sqrt[3]{z^2})^{1/3} ?

The solution to (27\sqrt[3]{z^2})^{1/3} is 3z^{2/9}

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simplify (27\sqrt[3]{z^2})^{1/3}

simplify

3 z^{\frac{2}{9}}

Solution steps

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

2 7^{\frac{1}{3}} = 3

Apply radical rule:

assuming

a \geq 0

= 3 (z^{\frac{2}{3}})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(z^{\frac{2}{3}})^{\frac{1}{3}} = z^{\frac{2}{3} \cdot \frac{1}{3}}

= 3 z^{\frac{2}{3} \cdot \frac{1}{3}}

\frac{2}{3} \cdot \frac{1}{3} = \frac{2}{9}

= 3 z^{\frac{2}{9}}

\frac{120}{72} \cdot 9

- x^{2} + 14 x = 48

(a^{\frac{1}{2}} \cdot b^{\frac{1}{3}})^{\frac{1}{2}}

2 x - 7 = - 3 x + 18

x^{3} - 8 y^{3}

What is (27\sqrt[3]{z^2})^{1/3} ?
The solution to (27\sqrt[3]{z^2})^{1/3} is 3z^{2/9}