Question

How do you simplify ${4^{ - 2}}$?

Answer 1

Hint:
The given question is to simplify the given process and exponents. Powers and exponent are nothing but to solve the powers of the given exponent which is in the order of higher power for example ${4^2}$, the method to solve this type of question is that to multiply $4$twice because the power $2$ means to multiply the limes and lunge we get $4 \times 4 = 16$

Complete step by step solution:
The given question is to find out the value of given exponent. Power or exponent is nothing but the higher order power of some other number but the power can also be negative.
In the given question, we had to solve or simplify, since power is also in the negative Hist of all we have to solve this negative hover. The rule to convert the power from negative to positive or positive to negative is to reciprocal the base which means ${\left( a \right)^{ - b}} = {\left( {\dfrac{1}{a}} \right)^b}$
If we reciprocal the base then the power changes from positive to negative or vice versa.
Now in given question, we have to simplify ${(4)^{ - 2}}$
Therefore ${(4)^{ - 2}}$ becomes ${\left( {\dfrac{1}{4}} \right)^2}$ in order to
Concert the power from negative to positive.
Now we have to simplify ${\left( {\dfrac{1}{4}} \right)^2}$which
means squaring of ${\left( {\dfrac{1}{4}} \right)^2}$ which means to multiply $\left( {\dfrac{1}{4}} \right)$ twice of we have to multiply
$\dfrac{1}{4} \times \dfrac{1}{4}$ which becomes $\dfrac{1}{{16}}$because $1 \times 1 = 1$ and $4 \times 4 = 16$
therefore, our question was to simplify ${(4)^{ - 2}}$firstly we had convert the power from negative to positive and then solve it by multiplying twice and hence we get $\dfrac{1}{{16}}$

Therefore ${(4)^{ - 2}}$ means $\dfrac{1}{{16}}$

Note:
The given question was to simplify the given power and exponent therefore we had to use the formula which was required. Along with that some more formulas for solving power and exponents is
\[{a^m} \times {a^n} = {a^{mn}}{\text{ and }}\dfrac{{{a^m}}}{{{a^n}}} = {a^{m - n}}\] Where $a$ , $b$,in and $c$ are any hyper of numbers either whole number, decimal or rational number.