Question

What is $-2$ to the $5th$ power?

Answer 1

Hint: To solve these types of questions which include numbers raised to certain powers or exponents, just simply multiply the given number as many times as the number power or exponent it is raised to and simplify to get the final answer.

Complete step by step solution:
The given information is,
We have been asked to find out what number we get, when we raise $-2$ to the $5th\;$ power. To calculate this, we simply have to multiply the given number, that is $-2$, $5$ times along with its sign to get our answer.
When we are given numbers with a negative or positive sign in front of them, then to check what sign would come in the final answer, we can use the following formula, which will help us to determine the sign of our final answer.
${{\left( -x \right)}^{n}}=\pm {{x}^{n}}$ , where $n$ represents the power or the exponent to which the number $x$ has been raised. The final answer will contain a $+$ or positive sign if the power, that is $n$, is even. On, the other hand, if the exponent or the power, that is $n$ , is an odd number then, the final answer will have a negative or $-$ in front of it.
Now, $-2$ to the $5th$ power can be written as ${{\left( -2 \right)}^{5}}$ . Here, if we compare the expression to the formula above, we get that $x=2$ and $n=5$ . Since, $n$ is an odd number, therefore, the final answer will have a negative or $-$ sign in front of it.
The next step will be to open the parenthesis and simplify the expression c, to get,
$\Rightarrow {{\left( -2 \right)}^{5}}=-2\times -2\times -2\times -2\times -2$
Further simplifying the above expression by multiplying all the terms, we get,
$\Rightarrow {{\left( -2 \right)}^{5}}=-32$
Hence, $-2$ to the $5th$ power will be given as $-32$

Note: While solving these questions, especially the ones where there is a sign involved pay extra attention to the multiplication of signs. Students often make mistakes while multiplying the signs and then end up with the wrong answers.