Question

Simplify. All variables represent nonnegative numbers.

(z^1/3)^3
————
sqrt(z^2)

Answer 1

`\large\underline{\mathbb{SOLUTION:}}`

We use the Power of Property formula for the numerator:

`\large{\boxed{ \\ \tt{ \purple{( {a}^(b) {)}^(c) = {a}^(bc) }}}}`

`\bullet\longrightarrow \tt{ = \frac{z (3)/(3) }{ \sqrt{ {z}^(2) } } }`

`\bullet\longrightarrow \tt{ = \frac{z }{ \sqrt{ {z}^(2) } } }`

Now, we need to apply this property for Radicals on the denominator:

`\bullet\longrightarrow \tt{ = \sqrt[n]{ {b}^(n) } = b }`

Thus we have,

`\bullet\longrightarrow \tt{ (z)/(z) = \boxed{ \purple{ \tt{1}}} }`

`\large\underline{\mathbb{ANSWER:}}`

`\therefore` The final answer is
`\small{\rm \boxed{ \purple{ \tt{1}}}}`.