the problem is 12 _ 2 _ 4 _ 3 =6
we have to use +, -, x, /, parentheses and use the exponents 2 or 3 once to make this true
Help
How about (12/2)/(4-3)?
Ah - whoops. Didn't see the condition that the exponents had to be used. Sorry.
Would you settle for (12/2)/(4-3)²? Or is there a limit on the number of times any operator can be used?
if you are 25 and you get 25 dollars every 2 wks and at the end of the month 10% is added like interest how much would you get if you stopped at 65 years old.
To solve this problem, we need to find the missing operators and the placements of parentheses, exponents, and numbers that will make the equation true.
Let's break it down step by step:
1. Exponents: We need to use either 2 or 3 as exponents once. Since there are no base numbers mentioned, we can conclude that the exponents will be applied to the numbers involved in the equation. To simplify the equation, we can focus on the left side, 12 _ 2.
2. Parentheses: We can use parentheses to group numbers and control the order of operations. Let's first use parentheses around 12 and 2, which gives us (12) _ (2).
3. Exponents (continued): Now, we can raise the result of 12 to an exponent of either 2 or 3. Let's consider 12^2 first. This gives us (12^2) _ (2).
4. Missing operator: We need to find a mathematical operator (+, -, x, or /) to fill in each underscore in the equation. To solve for the missing operator after the first underscore, we need to simplify the expression inside the parentheses first. So, (12^2) equals 144. The equation now becomes 144 _(2)_ (4)_(3)=6.
5. Missing operators and parentheses: Let's continue solving for the missing operators and parentheses. We can try different combinations to find a solution.
option a: If we use the division operator (/) for the first underscore, we have 144/2 = 72. The equation now becomes 72 _(4)_(3)=6. There is no combination of the remaining operators and parentheses that will make this equation true.
option b: If we use the addition operator (+) for the first underscore, we have 144 + 2 = 146. The equation now becomes 146 _(4)_(3)=6. Again, there is no combination of the remaining operators and parentheses that will make this equation true.
option c: If we use the subtraction operator (-) for the first underscore, we have 144 - 2 = 142. The equation now becomes 142 _(4)_(3)=6. Similarly, there is no combination of the remaining operators and parentheses that will make this equation true.
option d: If we use the multiplication operator (x) for the first underscore, we have 144 x 2 = 288. The equation now becomes 288 _(4)_(3)=6.
6. Missing operators and parentheses (continued): Now we need to solve for the missing operator after the second underscore. Let's try different combinations:
option d.1: If we use the division operator (/) after the second underscore, we have 288 / 4 = 72. The equation now becomes 72 _(3)=6. There is no combination of the remaining operator and parentheses that will make this equation true.
option d.2: If we use the addition operator (+) after the second underscore, we have 288 + 4 = 292. The equation now becomes 292 _(3)=6.
option d.3: If we use the subtraction operator (-) after the second underscore, we have 288 - 4 = 284. The equation now becomes 284 _(3)=6. Again, there is no combination of the remaining operator and parentheses that will make this equation true.
option d.4: If we use the multiplication operator (x) after the second underscore, we have 288 x 4 = 1152. The equation now becomes 1152 _(3)=6. This can be solved by raising 1152 to an exponent of 3. So, 1152^3 = 1,620,787,200. Therefore, the equation becomes 1620787200 = 6, which is not true.
7. Conclusion: After exploring different combinations of operators and parentheses, it appears that there is no combination that will make the equation 12 _ 2 _ 4 _ 3 = 6 true using +, -, x, /, parentheses, and the exponents 2 or 3 once. It is possible that no solution exists for this specific equation.