Question

How do you simplify \[{8^{ - 2}}\]?

Answer 1

Hint: In the above question we are provided with an exponential number that is \[{8^{ - 2}}\] and we are asked the method to simplify that so for approaching such kind of questions one should firstly have a knowledge about the exponential numbers or the exponential form of a number that is the form like \[{t^a}\] where \[t\] is the base \[a\] to which a certain power is raised which represent the certain number where both \[t\] and \[a\] can be both negative and positive.

Complete step-by-step answer:
In the above question we are given \[{8^{ - 2}}\] an exponential form (that is the form like \[{t^a}\] where \[t\] is the base \[a\] to which a certain power is raised which represent the certain number where both \[t\] and \[a\] can be both negative and positive). And we are asked to simplify that.
So we would simplify and solve the given exponential form \[{8^{ - 2}}\] by using the exponential formulas to solve the given exponential
So using the formula of the exponents to solve the above given exponents that is –
\[{t^{ - a}} = \dfrac{1}{{{t^a}}}\] (as the exponent is raised to a power in the negative form the exponent becomes the fraction with the exponent that is given to us in the denominator and the \[1\] as the numerator of the fraction making the power to which the exponent is having as positive)
Now applying the above formula on the given exponential \[{8^{ - 2}}\] it comes out to be-
$\Rightarrow$ \[{8^{ - 2}} = \dfrac{1}{{{8^2}}}\]
Now further solving the above resultant that is the \[{8^2} = 64\]
The above result becomes –
$\Rightarrow$ \[{8^{ - 2}} = \dfrac{1}{{64}}\]
So the required simplification of the given exponent in the question is the \[\dfrac{1}{{64}}\]

Note: While doing such kinds of the questions one should know the basic formulas different representations of the one exponential form to the other. These formulas are the key to solving these questions. Also care should be taken while solving these as the mistake while simplification can result in a wrong answer.