Question 1
2*3-4/5^-2
Adam wrote:
2*5 ^2/3^4
Nick wrote: 5^2//2*3^4
Shane wrote:
2*3^4/5^2
Who is correct and why
2*3-4/5^-2
= 8 - 4*5^2
= 8 - 4*25
= 8 - 100
= -92
Adam's answer = 2*5 ^2/3^4
= 2*25/81
= 50/81 ≠ -92
Nick wrote: 5^2//2*3^4 , which makes no sense due to the //
Shane wrote: 2*3^4/5^2
= 2*81/25
= 162/25 ≠ -92
Fix you post, or else it makes no sense
To determine who is correct, let's simplify the expression step by step using the order of operations, which states that you should perform operations inside parentheses first, then exponentiation, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Original expression: 2*3 - 4/5^-2
First, we have an exponentiation operation: 5^-2.
Recall that any number raised to a negative exponent is equivalent to 1 divided by that number raised to the positive exponent. Therefore, 5^-2 is equal to 1 / 5^2.
Simplifying further:
2*3 - 4 / (1 / 5^2)
Next, let's evaluate the exponentiation:
2*3 - 4 / (1 / 25)
Continuing with multiplication and division from left to right:
6 - 4 / (1 / 25)
Now, let's solve the division:
6 - 4 * 25
Multiplication takes precedence over subtraction:
6 - 100
Finally, perform the subtraction:
-94
After simplifying the expression step by step, we get -94.
Comparing the original expressions:
Adam: 2*5^2 / 3^4 = 50 / 81 (incorrect)
Nick: 5^2 // 2 * 3^4 = 25 // 2 * 81 (incorrect)
Shane: 2*3^4 / 5^2 = 2*81 / 25 = 162/25 (correct)
Among Adam, Nick, and Shane, the correct answer is given by Shane, who simplified the expression correctly to 162/25.