We are asked to evaluate the given expression and then change the signs so that its value is 8. Let's solve one task at a time.
Evaluate the Expression
We are given the following expression.
14+5*3+3^2
To evaluate it, we need to follow the order of operations. First, we will calculate the power, then the product, and only then the sum and difference.
There are many ways to start looking for another expression whose value is 8. However, we can only change two operation signs in the original expression. Notice that 3^2 = 9 will always be calculated first, so we can just keep this written as 9.
14 5 3 3^2
⇓
14 5 3 9
We have three possible spaces to use any operation sign, but we can only modify two signs from the original expression. Let's fill one of the spaces and see what can we do with the remaining ones. For example, we can rewrite the multiplication sign between 5 and 3.
14 5 * 3 9
Since all the numbers are greater than 8, using a multiplication sign inside one the boxes will only take us further away from our goal. We cannot use a division sign either, since the result wouldn't be an integer. This leaves us with either addition or subtraction.
14 ± 5 * 3 ± 9
According to the order of operations, multiplication is performed before subtraction and addition, so 5* 3= 15 will be the next step calculated. Now we will work with the following expression.
14 ± 15 ± 9
Notice that 15 is just one unit greater than 14, and 9 is just one unit greater than 8. Hence, subtracting 15 from 14 will get us - 1, and adding it to 9 will result in 8.
14 - 15 + 9
= 8
Therefore, the expression that evaluates to 8 is 14-3 * 5+3^2.
