What is the value of n?

Question

asked Feb 18, 2023 225k views

1 Answer

Hervey · Answer 1 · 2023-02-24T19:13:34+0000

Answer:

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

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)