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5.1: Ufafanuzi wa a

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    164577

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    Ufafanuzi:\(a^n\)

    Kwa idadi yoyote halisi\(a\) na idadi nzuri\(n\),\(a^n\) ni kuzidisha mara kwa mara ya\(a\) kwa\(n\) mara yenyewe.

    \[a^n= a\cdot a \cdot a\cdot a\cdot a\cdot a\cdot a\cdot a \ldots \ldots \cdot a \nonumber \]

    Nukuu:

    \(a\)ni msingi,\(n\) ni exponent chanya.

    \(a^n\)ni kusoma kama”\(a\) alimfufua kwa nguvu ya\(n\).”

    Mfano Template:index

    Kutambua msingi na exponent katika maneno.

    \(2^4\)\(x^5\),\(\left(\dfrac{3}{7}\right)^7\),\((-3)^3\)

    Suluhisho
    Ufafanuzi Msingi Mtetezi
    \(2^4\) 2 4
    \(x^5\) \(x\) 5
    \(\left(\dfrac{3}{7}\right)^7\) \(\dfrac{3}{7}\) 7
    \((-3)^3\) -3 3
    Tatizo la mazoezi

    Kutambua msingi na exponent ya yafuatayo.

    Ufafanuzi Msingi Mtetezi
    \(7^9\)
    \((-11)^6\)
    \(a^b\)
    \(\left(\dfrac{11}{12}\right)^5\)
    \(12^3\)
    \(\left(-\dfrac{7}{3}\right)^2\)
    \(x^7\)
    \((2.56)^4\)

    Kutathmini maneno ya fomu\(a^n\)

    Wakati msingi na exponent ni thamani namba inawezekana kutathmini usemi imeandikwa katika na exponent. Ili kupata thamani, tumia ufafanuzi na kupanua maneno. Mara baada ya kupanua, kuzidisha na matokeo ni thamani ya namba ya kujieleza.

    Mfano Template:index

    Panua maneno yafuatayo na tathmini ikiwa inawezekana.

    \(3^4\),\(\left(\dfrac{3}{5}\right)^3\)\(x^7\),\((3.12)^2\),\((-5)^3\),\((-y)^6\)

    Suluhisho
    \(3^4\) \(= 3\cdot 3\cdot 3\cdot 3 = 81\)
    \(\left(\dfrac{3}{5}\right)^3\) \(\dfrac{3 }{5} \cdot \dfrac{3}{ 5 }\cdot \dfrac{3 }{5} = \dfrac{27 }{125}\)
    \(x^7\)

    \(x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\)

    Kumbuka: Haiwezi kutathmini tangu x haijulikani
    \((3.12)^2\) \((3.12)\cdot (3.12) = 9.734\)
    \((-5)^3\) \(−5 \cdot −5 \cdot −5 = −12\)
    \((-y)^6\)

    \(−y \cdot −y \cdot −y \cdot −y \cdot −y \cdot −y = y^6\)

    Kumbuka: y haijulikani
    Zoezi Template:index

    Panua maneno yafuatayo na tathmini ikiwa inawezekana.

    1. \(7^3\)
    2. \(\left(−\dfrac{ 2 }{3}\right)^4\)
    3. \((−x)^7\)
    4. \((7.14)^2\)
    5. \((−3)^9\)
    6. \((z)^5\)
    7. \(\left(− \dfrac{11 }{33 }\right)^2\)
    8. \(6^5\)
    9. \(\left(\dfrac{x}{ y}\right)^4\)
    10. \(a^{10}\)
    11. \(\left(\dfrac{2}{x}\right)^3\)