Question

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

Answer 1

Answer:

The solution is;

$\frac{130}{3969}$

Explanation:

Given the expression;

$(-9)^{-2}+(-7)^{-2}$

Recall that from the laws of indices;

$x^{-a}=\frac{1}{x^a}$

Applying to the above case;

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

So we can now simplify;

$\begin{gathered} =\frac{1}{(-9\times-9)}+\frac{1}{(-7\times-7)} \\ =\frac{1}{81}+\frac{1}{49} \end{gathered}$

So, we can now add;

$\begin{gathered} \frac{1}{81}+\frac{1}{49} \\ =\frac{49+81}{81(49)} \\ =\frac{130}{81(49)} \\ =\frac{130}{3969} \end{gathered}$

Therefore, the solution is;

$\frac{130}{3969}$