Question

If \[{5^{ - 2}}\] is equal to \[\dfrac{1}{{\text{k}}}\] then k is equal to?

Answer 1

Hint: In order to find the value of k we first need to write the given equation and then just cross multiply the elements to get the value of k.

Complete step-by-step answer:
First of all we will write the given equation:
\[{5^{ - 2}} = \dfrac{1}{{\text{k}}}\]
Cross multiplying both sides we get:
\[{5^{ - 2}}{\text{k = 1}}\]
Further solving the above equation we get:
\[
  \dfrac{{\text{k}}}{{{5^2}}} = 1 \\
  \dfrac{{\text{k}}}{{25}} = 1 \\
  {\text{k}} = 25 \\
 \]
Therefore we get the value of k as 25.

Note: This question can also be solved directly by taking the reciprocal of both the side as:
  \[\dfrac{1}{{{5^2}}} = \dfrac{1}{{\text{k}}}\]
Now taking reciprocal of both the sides we get:
\[
  {\text{k}} = {5^2} \\
  {\text{k}} = 25 \\
 \]