Question

`{( - 9)}^( - 2) + {( - 7)}^( - 2) =`how do you solve this

Answer 1

The solution is;

`(130)/(3969)`

Step-by-step explanation:

Given the expression;

`(-9)^(-2)+(-7)^(-2)`

Recall that from the laws of indices;

`x^(-a)=(1)/(x^a)`

Applying to the above case;

`\begin{gathered} (-9)^(-2)+(-7)^(-2) \\ =(1)/((-9)^2)+(1)/((-7)^2) \end{gathered}`

So we can now simplify;

`\begin{gathered} =(1)/((-9*-9))+(1)/((-7*-7)) \\ =(1)/(81)+(1)/(49) \end{gathered}`

So, we can now add;

`\begin{gathered} (1)/(81)+(1)/(49) \\ =(49+81)/(81(49)) \\ =(130)/(81(49)) \\ =(130)/(3969) \end{gathered}`

Therefore, the solution is;

`(130)/(3969)`