Question

Rewrite the expression in the form z^n

Answer 1

`z^{ (1)/(3)`

Explanation:

`\sqrt{\frac{z}{z^{(1)/(3)} } } = \sqrt{z * z^{-(1)/(3)}`
`[ \ (a)/(a^x) = a \cdot a^(-x) \ ]`

`= \sqrt {z^{(2)/(3)}}\\\\`
`[ \ a^x \cdot a^y = a^( x+ y) \ ]`

`= (z^{(2)/(3)})^{ (1)/(2)}`
`[ \ √(x^y) = (x^(y)) ^{(1)/(2)} \ ]`

`= z^ {(1)/(3)}`
`[ \ (a^x)^y = a^(xy) \ ]`