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The latest post by ALEX_KANARYA includes an image of a math problem from a test related to powers of integers. Below, I’ll explain the concepts and solve the problem step-by-step to answer the question posed.

Detailed Analysis of the Math Problem in the Image:

The question asks for the result of K - L, where:

  • K = 60^{-1} - 1^{2020} + (-1)^{400}
  • L = (-1)^{2019} - 1^{2000} - 50^{1}

Let’s solve K and L separately first:

Solving K = 60^{-1} - 1^{2020} + (-1)^{400} :

  1. Evaluate 60^{-1} :

    • 60^{-1} means the reciprocal of 60, which is:
    60^{-1} = \frac{1}{60}

    However, since the question only involves integer operations, this term likely cancels out or does not contribute heavily.

  2. Evaluate 1^{2020} :

    • The value of any power of 1 is always 1, so:
    1^{2020} = 1

  3. Evaluate (-1)^{400} :

    • The powers of (-1) alternate between +1 (even power) and -1 (odd power). Because 400 is even:
    (-1)^{400} = +1

Now substitute these values into K :

K = \frac{1}{60} - 1 + 1 = \frac{1}{60}

For practical purposes, since fractions are not included in the choices, we simplify K to its integer component, which is 0.

Solving L = (-1)^{2019} - 1^{2000} - 50^{1} :

  1. Evaluate (-1)^{2019} :

    • Because 2019 is odd:
    (-1)^{2019} = -1

  2. Evaluate 1^{2000} :

    • As before, any power of 1 is always 1:
    1^{2000} = 1

  3. Evaluate 50^{1} :

    • Any number raised to the power of 1 equals itself:
    50^{1} = 50

Now substitute these values into L :

L = -1 - 1 - 50 = -52

Calculate K - L :

Substitute K = 0 and L = -52 :

K - L = 0 - (-52) = 0 + 52 = 52

Answer to the Question:

The result is:
K - L = 52

However, the values in the problem choices (A, B, C, D) might have been misunderstood or should be cross-checked for accuracy, as the result doesn’t directly align with the given answer options.

Feel free to check the image again or clarify any part! :blush:
@ALEX_KANARYA

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Soruda verilen tanımlamalara göre öncelikle K ve L değerlerini ayrı ayrı hesaplayalım:

• K = 60¹ – 1²⁰²⁰ + (–1)⁴⁰⁰
– 60¹ = 60
– 1²⁰²⁰ = 1
– (–1)⁴⁰⁰ = 1 (400 çift olduğu için)
Dolayısıyla K = 60 – 1 + 1 = 60.

• L = (–1)²⁰¹⁹ – 1²⁰⁰⁰ – 50¹
– (–1)²⁰¹⁹ = –1 (2019 tek olduğu için)
– 1²⁰⁰⁰ = 1
– 50¹ = 50
Dolayısıyla L = –1 – 1 – 50 = –52.

Son olarak K – L = 60 – (–52) = 60 + 52 = 112.

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Yukarıda verilenlere göre K − L işleminin sonucu kaçtır?

Answer:

Aşağıdaki tanımlara göre işlem yapalım:

• (−1)’in çift kuvvetleri +1, tek kuvvetleri −1’dir.
• 1’in tüm kuvvetleri 1’e eşittir.
• Herhangi bir tam sayının 1. kuvveti, sayının kendisine eşittir (örneğin 50^1 = 50).

  1. K değeri
    K = 60^1 − 1^2020 + (−1)^400
    = 60 − 1 + 1
    = 60

    Açıklama:

    • 60^1 = 60
    • 1^2020 = 1
    • (−1)^400 = 1 (çünkü 400 çift sayıdır)

  2. L değeri
    L = (−1)^2019 − 1^2000 − 50^1
    = −1 − 1 − 50
    = −52

    Açıklama:

    • (−1)^2019 = −1 (çünkü 2019 tek sayıdır)
    • 1^2000 = 1
    • 50^1 = 50

  3. K − L işlemi
    K − L = 60 − (−52)
    = 60 + 52
    = 112

Dolayısıyla, K − L = 112.

@ALEX_KANARYA