Question

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

Answer 1

Hint: In this problem we need to evaluate the value of \[ - {2^4}\] . Now we know that for a positive integer \[n\] we have \[{a^n} = a \times a \times a \times ...n{\text{ }}times\] . So, we will use this property to expand the given power. Then we will just multiply them individually and hence find the value of \[ - {2^4}\].

Complete step by step answer:
We are given that we have to simplify \[ - {2^4}\]
Now, we know that for a positive integer \[n\] we have
\[{a^n} = a \times a \times a \times ...n{\text{ }}times\]
So here, \[a = 2\] and \[n = 4\]
Therefore, we get as
\[ - {\left( 2 \right)^4} = - \left( {2 \times 2 \times 2 \times 2} \right)\]
Now, we will club the first \[2's\] together and last \[2's\] together, then we will get the following expression as:
\[ - {\left( 2 \right)^4} = - \left( {\left( {2 \times 2} \right) \times \left( {2 \times 2} \right)} \right)\]
Now, we know that \[2 \times 2 = 4\]
Therefore, we get the following expression as:
\[ - {\left( 2 \right)^4} = - \left( {4 \times 4} \right)\]
Now, finally simplify the bracket, we get
\[ - {\left( 2 \right)^4} = - 16\]
Hence, \[ - {2^4}\] equals to \[ - 16\]
which is the required result.

Note:
 The given question is in exponential form. An exponential equation is those equations in which variables occur as exponents. An exponent refers to the number of times a number is multiplied by itself. There is a base and an exponent in this type of equation. Here the number \[2\] is called the base, and the number \[4\] is called the exponent or index.
Also note that the possibility of a mistake while doing this question is that we might raise power \[4\] to the \[ - 2\] instead of \[2\].
If we do this, we get the answer as
\[{\left( { - 2} \right)^4} = \left( { - 2 \times - 2 \times - 2 \times - 2} \right)\]
and we know that
\[\left( { - a} \right) \times \left( { - a} \right) = a\]
Therefore, we get
\[ \Rightarrow {\left( { - 2} \right)^4} = 16\]
which is the wrong answer. So, take care of this thing while doing the question because in the question we have given \[2\] is raised to the power of \[4\] not \[ - 2\] is raised to the power of \[4\] .If they wanted to do that they would write \[{\left( { - 2} \right)^4}\]