Question

Which number is equivalent to \[{5^{ - 1}}\]?

Answer 1

Hint: In order to solve this question first, we assume a variable that is equal to the given number. Then we use the general rule of power that is if power is negative then that power becomes positive if the number goes into the denominator. And then expand the power in order to get the answer.

Complete step-by-step answer:
Given, the number in exponential form \[{5^{ - 1}}\].
Let, the given value be equal to \[x\].
\[x = {5^{ - 1}}\]
Now we use the general rule of the power \[{x^{ - a}} = \dfrac{1}{{{x^a}}}\].
Here in this rule \[x = 5\] and \[a = - 1\]
On using this rule the equation be like.
\[x = \dfrac{1}{{{5^1}}}\]
Now we expand the power of the given equation:
We know that anything powerful one equal to that number. \[{y^1} = y\]
Here \[y = 5\]
On expanding power of the given equation.
\[x = \dfrac{1}{5}\]
Final answer:
\[\dfrac{1}{5}\] is the number which is equivalent to \[{5^{ - 1}}\]
\[{5^{ - 1}} = \dfrac{1}{5}\]

Note: Although this question is very simple nothing is advanced in this but students must know the rules of the power. Negative power can not expand directly. In order to expand that power we have to first take that part in the denominator and then we have to expand the power. If the answer asked in the question is in the decimal form then also the same steps are taken and at last, we will divide that part in order to get the answer in the decimal form. In this question, we have to find equivalent numbers so if we keep that part infraction in decimal we are able to find the exact value.