Question

What is the value of n?

Answer 1

`n = { \boxed{ - (2)/(3) }}`

Explanation:

`\frac{1}{( {\sqrt[3]{5}})^(2) } = {5}^(n) \\`

- Change or convert the cube root into an index form; ³√x = x^⅓

`\frac{1}{( {5}^{ (1)/(3) }) {}^(2) } = {5}^(n) \\`

- Open the brackets by multiplying the powers; (a²)² = a²×²

`\frac{1}{ {5}^{( (1)/(3) * 2)} } = {5}^(n) \\ \\ \frac{1}{ {5}^{ (2)/(3) } } = {5}^(n)`

- Following the law of indices below;

`{ \boxed{ \blue{ \pmb{( \frac{1}{ {x}^(a) } ) = {x}^( - a) }}}}`

- Therefore;

`{5}^{ - (2)/(3) } = {5}^(n) \\`

- Since the bases (5) are the same, the powers are equal;

`n = - (2)/(3)`