지수의 확장: 유리수의 지수 #

지수의 확장 #

지수가 유리수인 경우 #

anm=anma^{\frac{n}{m}} = \sqrt[m]{a^n}

원리 #

  • 271/327^{1/3}

    1. 271/3=271327^{1/3}=\sqrt[3]{27^1}
    2. x∗x∗x=27x * x * x = 27
    3. x=3x = 3
    4. 33=273^3 = 27

  • 641/664^{1/6}

    1. 641/6=641664^{1/6}=\sqrt[6]{64^1}
    2. x∗x∗x∗x∗x=64x * x * x * x * x = 64
    3. x=2x = 2
    4. 25=642^5 = 64

  • x1/2x^{1/2}

    • x3=x∗x∗xx^{3} = x * x * x
    • x2=x∗xx^{2} = x * x
    • x1=xx^{1} = x
    • x1/2=x2x^{1/2} = \sqrt[2]{x}
      • x=x∗xx = \sqrt{x} * \sqrt{x}
    • x1/3=x3x^{1/3} = \sqrt[3]{x}

  • 1001.5=1003/2=10032=1001022=100∗10100^{1.5} = 100^{3/2} = \sqrt[2]{100^3} = 100\sqrt[2]{10^2} = 100 * 10

  • 1001.5=1003/2=(1003)0.5=(1003)1/2=10032=1001022=100∗10100^{1.5} = 100^{3/2} = ({100^3})^{0.5} = ({100^3})^{1/2} = \sqrt[2]{100^3} = 100\sqrt[2]{10^2} = 100 * 10

(지수 = 12\frac{1}{2}) #

  • 41/2=412=24^{1/2} = \sqrt[2]{4^1} = 2
  • 81/4=814≈1.6828^{1/4} = \sqrt[4]{8^1} ≈ 1.682