Question

How do you simplify \[\dfrac{1}{{{4^{ - 2}}}}\]?

Answer 1

Hint: In the given question, we have been asked to calculate a given expression. To solve the question, we need to know how to convert a negative exponential power to a positive exponential power. We do that, and then we just solve the exponent as normal.

Formula Used:
To solve the question, we are going to use the formula to convert a negative exponential power to a positive exponential power, which is,
\[{a^{ - b}} = \dfrac{1}{{{a^b}}}\]
or \[\dfrac{1}{{{a^{ - b}}}} = {a^b}\]

Complete step by step answer:
In the question, the expression to be solved is \[\dfrac{1}{{{4^{ - 2}}}}\].
First, we convert the negative power to positive,
\[\dfrac{1}{{{4^{ - 2}}}} = {4^2}\]
Now, we just solve the expression as normal,
\[{4^2} = 4 \times 4 = 16\]

Additional Information:
So, if the power is negative, we inverse the number and solve the exponent normally. But, if the power is a fraction, then it is a root exponent, for example, \[{a^{\dfrac{1}{3}}} = \sqrt[3]{a}\]. Hence, if we have a number of the form \[{a^{\dfrac{m}{n}}}\], then it can be written as,
\[\sqrt[n]{{{{\left( a \right)}^m}}}\]

Note: The negative power only affects the fraction kind of thing of the number. It does not change anything about the sign with the number. So, if we have negative power, we just take the reciprocal of the number and calculate the number normally.