Üslü Sayılar Formülleri – Kurallar

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Üslü ifadeler ile ilgili formüller, kurallar. Üslü sayıların özellikleri, kuralları.

Üslü İfadeler;

a ∈ R ve n ∈ N+ olmak üzere, a.a.a.a….a = an dir. Bu eşitlikte a ya taban, n ye üs denir.

Üslü Sayılar Formülleri – Kurallar

\displaystyle \begin{array}{l}*a\ne 0\\{{a}^{0}}=1\end{array}

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\displaystyle \begin{array}{l}*{{\left( -a \right)}^{2n}}={{a}^{2n}}\\{{\left( -a \right)}^{2n-1}}=-{{a}^{2n-1}}\end{array}

\displaystyle *a.{{x}^{n}}\mp b{{x}^{n}}=\left( a\mp b \right){{x}^{n}}

\displaystyle \begin{array}{l}*{{a}^{n}}.{{a}^{m}}={{a}^{n+m}}\\{{a}^{n}}.{{b}^{n}}={{\left( a.b \right)}^{n}}\end{array}

\displaystyle \begin{array}{l}*\frac{{{a}^{n}}}{{{a}^{m}}}={{a}^{n-m}}\to \left( a\ne 0 \right)\\\frac{{{a}^{n}}}{{{b}^{n}}}={{\left( \frac{a}{b} \right)}^{n}}\to \left( b\ne 0 \right)\end{array}

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\displaystyle \begin{array}{l}*{{a}^{-n}}=\frac{1}{{{a}^{n}}}\\{{\left( \frac{a}{b} \right)}^{-n}}={{\left( \frac{b}{a} \right)}^{n}}\end{array}

\displaystyle *{{\left( {{a}^{m}} \right)}^{n}}={{\left( {{a}^{n}} \right)}^{m}}={{a}^{m.n}}

\displaystyle \begin{array}{l}*{{a}^{n}}={{a}^{m}}\Rightarrow n=m\\\left( a\ne 0,a\ne 1,a\ne -1 \right)\end{array}

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