Find the value of the following expression:
(2^8 ⋅ 5−5 ⋅ 19^0)−2 ⋅ (5-2/2^3)^4 ⋅ 2^28 (5 points)
Write your answer in simplified form. Show all of your steps. (5 points)
Please somebody help me I'm so confused. I know I'm supposed to use PEMDAS and I know 2^8= 25, 19^0=1, 2^3=8, and 2^28= 268435456.The rest I have no idea what to do. I would really appreciate it if somebody could help! :/
I saw this one posted earlier, as
(2^8 ⋅ 5^−5 ⋅ 19^0)^−2 ⋅ (5^-2/2^3)^4 ⋅ 2^28
= (2^-16 ⋅ 5^10 ⋅ 1)⋅(5^-8 / 2^12) ⋅ 2^28
= 2^(-16-12+28) ⋅ 5^(10-8)
= 2^0 ⋅ 5^2
= 1 ⋅ 25
= 25
You need to get your typing in order if you want to get the right answer.
No problem! I can help you step-by-step with evaluating the given expression. Let's start by breaking it down and simplifying each part:
Step 1: Simplify the exponents.
- 2^8 = 256
- 19^0 = 1 (Any number raised to the power of 0 is always 1)
- 2^3 = 8
- 2^28 = 268435456
Now let's rewrite the expression with these simplified values:
(256 ⋅ 5−5 ⋅ 1)−2 ⋅ (5-2/8)^4 ⋅ 268435456
Step 2: Perform multiplication and division from left to right.
Here, we have two multiplication and division operations:
256 ⋅ 5 = 1280
5 - 5 ⋅ 1 = 5 - 5 = 0
Now we can rewrite the expression:
(1280 - 0)−2 ⋅ (5-2/8)^4 ⋅ 268435456
Step 3: Evaluate the parentheses.
Inside the parentheses, we have (5 - 2/8)^4. Let's simplify it:
5 - 2/8 = 5 - 1/4 = 4 3/4
Now rewrite the expression again:
(1280 - 0)−2 ⋅ (4 3/4)^4 ⋅ 268435456
Step 4: Evaluate the exponent.
(4 3/4)^4 can be simplified as follows:
(4 3/4)^4 = (19/4)^4 = (19^4)/(4^4) = 130321/256
Rewrite the expression:
(1280 - 0)−2 ⋅ (130321/256) ⋅ 268435456
Step 5: Perform multiplication and division from left to right.
Here, we have two multiplication and division operations:
(1280 - 0) = 1280
1280 ** -2 = 1/1280^2 = 1/1638400
Now we can rewrite the expression:
(1/1638400) ⋅ (130321/256) ⋅ 268435456
Step 6: Simplify the fractions.
To multiply fractions, we multiply the numerators together and the denominators together:
(1 * 130321) / (1638400 * 256) = 130321 / 419430400
Let's rewrite the expression:
(130321 / 419430400) ⋅ 268435456
Step 7: Perform multiplication.
Multiply the numerators together and the denominators together:
130321 * 268435456 = 34912248435136
419430400 * 1 = 419430400
So the expression simplifies to:
34912248435136 / 419430400
Finally, we can simplify the fraction:
34912248435136 / 419430400 = 832973.5
Sure, I can help you solve this expression step by step using the order of operations (PEMDAS).
Here's the given expression:
(2^8 ⋅ 5−5 ⋅ 19^0)−2 ⋅ (5-2/2^3)^4 ⋅ 2^28
Step 1: Simplify the exponents.
We know that 2^8 equals 256, 19^0 equals 1, 2^3 equals 8, and 2^28 equals 268,435,456. Substituting these values, the expression becomes:
(256 ⋅ 5 − 5 ⋅ 1)−2 ⋅ (5 − 2/8)^4 ⋅ 268435456
Step 2: Perform the multiplications and the subtraction inside the parentheses.
We have:
(1280 − 5)−2 ⋅ (5 − 0.25)^4 ⋅ 268435456
Simplifying further:
1275^−2 ⋅ (4.75)^4 ⋅ 268435456
Step 3: Evaluate the exponent.
To calculate 1275^−2, we can first find the reciprocal of 1275, which is 1/1275. Then, we square this reciprocal:
(1/1275)^2 ⋅ (4.75)^4 ⋅ 268435456
The reciprocal of 1275 is 1/1275, and 1/1275 squared is 1/1625625.
(1/1625625) ⋅ (4.75)^4 ⋅ 268435456
Step 4: Evaluate the remaining multiplication and exponentiation.
Now we need to evaluate (4.75)^4. Raising 4.75 to the power of 4 gives us 357.40625.
(1/1625625) ⋅ 357.40625 ⋅ 268435456
Step 5: Perform the final multiplication.
Now we just need to multiply the resulting values to get the final answer:
(1/1625625) ⋅ 357.40625 ⋅ 268435456 ≈ 511998.4
So the value of the given expression is approximately 511998.4.
I hope this explanation helps you understand how to solve the expression. Let me know if you have any further questions!