Question

How do you simplify ${\left( { - 4} \right)^2}?$

Answer 1

Hint:
The given question is to simplify the given powers and exponents. Power and exponents are nothing but to solve the power 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 to multiply $4$ twice because the power $2$ means to multiply two times and hence we get $4 \times 4 = 16$.

Complete Step by step Solution:
The given question is to find out the value of a given component. Power or exponent is nothing but the higher order power of some other number. But the power can be of any order as well as the power can also be negative.
In the given question we had to solve or simplify${\left( { - 4} \right)^2}$. We had to make the question very clear that what is the difference between $ - {\left( 4 \right)^2}{\text{ and }}{\left( { - 4} \right)^2}$, First one means we have to do the square which is ${4^2} - 16$ and negative sign remains as it is which means $ - {\left( 4 \right)^2}{\text{ means }} - 16$. But the second one is that $ - {\left( 4 \right)^2}$ which means negative sign is inside the bracket where term in the bracket is to multiply twice which means the whole term along with the negative sign is multiplied twice.
Therefore $ - {\left( 4 \right)^2}$means$\left( { - 4} \right) \times \left( { - 4} \right)$. Since negative sign when multiplied by negative. Sign, we get positive signs and$\left( { - 4} \right) \times \left( { - 4} \right) = 16$.

Hence the question was to simplify ${\left( { - 4} \right)^2}$ which means$16$.

Note:
The given question was to simplify the given power and exponent. Therefore we had used the formula which was required. Along with that some more formulas for solving powers and exponents is
\[{a^m} \times {a^n} = {a^{m + n}}{\text{ and }}\dfrac{{{a^{{n_1}}}}}{{{a^n}}} \times {a^{m - n}}\]
Where $a,b,m{\text{ and }}n$any are a type of number either whole number, decimal or rational number.