CRITICAL THINKING: Witout grouping symbols,the expression 2.3³+4 had a value of 58.Insert grouping symbols in the expression 2.3³ + 4 to produce the following values :
1. 62
2. 220
3. 4374
4. 279,936
Thanks ,please help me,i don't know what to do.
2*(3^3 + 4)
(2 * 3)^3 + 4
2 * 3^(3 + 4)
(2 * 3)^(3 + 4)
To solve this problem, we need to insert grouping symbols in the expression 2.3³ + 4 to achieve the given values. Let's break it down step by step for each value:
1. To obtain a value of 62:
Since the value without grouping symbols is 58, we need to increase it by 4. One way to achieve this is by adding grouping symbols to only the exponent. We can write it as (2.3)³ + 4, which simplifies to (2.3)*(2.3)*(2.3) + 4. Now, let's calculate this expression:
(2.3)*(2.3)*(2.3) + 4 = 12.167 + 4 = 16.167
As 16.167 is not equal to 62, this is not the correct solution.
2. To obtain a value of 220:
Again, the value without grouping symbols is 58, so we need to increase it by 162. One way to achieve this is to put a set of parentheses around the entire expression: (2.3³ + 4). Now, let's calculate this expression:
(2.3³ + 4) = (2.3)*(2.3)*(2.3) + 4 = 12.167 + 4 = 16.167
As 16.167 is not equal to 220, this is not the correct solution.
3. To obtain a value of 4374:
This time, we need to increase the value by a significant amount, 4316. To accomplish this, we can add grouping symbols around both the base number and the exponent: (2.3)^(³ + 4). Now, let's calculate this expression:
(2.3)^(³ + 4) = (2.3)^(3 + 4) = (2.3)^7 = 4374
As the expression equals 4374, this is the correct solution.
4. To obtain a value of 279,936:
Here, we need to increase the value by a substantial amount, 279,878. One way to achieve this is to put a set of parentheses around the base number and raise the entire expression to the power of 3: (2.3^³) + 4. Now, let's calculate this expression:
(2.3^³) + 4 = (2.3)^3 + 4 = 12.167 + 4 = 16.167
As 16.167 is not equal to 279,936, this is not the correct solution.
Therefore, the answer is:
3. (2.3)^(³ + 4) = 4374.