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IMG-d0ced6f67e9e725f70662e7011ce32d8-V.jpg (79.78 KiB) Прегледано 342 пъти

ми

[ammornil]

$$a^{0}=1, (a\ne 0)\hspace{2em} a^{\normalsize{m}}\cdot{a^{\normalsize{n}}}=a^{\normalsize{m+n}}\hspace{2em} \frac{a^{\normalsize{m}}}{a^{\normalsize{n}}}=a^{\normalsize{m-n}}, (a\ne 0) \hspace{2em} a^{\normalsize{-m}}=\frac{1}{a^{\normalsize{m}}}, (a\ne 0) \hspace{2em}(a^{\normalsize{m}})^{\normalsize{n}}=a^{\normalsize{m\cdot{n}}} $$
минус на четна степен се преобразува в плюс; минус на нечетна степен остава минус.

$$ \begin{aligned} \text{A} \rightarrow & 4 \\ \text{Б} \rightarrow & 1 \\ \text{В} \rightarrow & 3 \end{aligned} $$

(A) [tex]\hspace{2em}\frac{3^{7}\cdot{2^{7}}}{6^{3}\cdot{(-36)^{2}}}=\frac{(3\cdot{2})^{7}}{6^{3}\cdot{(36)^{2}}}=\frac{6^{7}}{6^{3}\cdot{(6^{2})^{2}}}=\frac{6^{7}}{6^{3}\cdot{6^{2\cdot 2}}}=\frac{6^{7}}{6^{3}\cdot{6^{4}}}=\frac{6^{7}}{6^{3+4}}=\frac{6^{7}}{6^{7}}=1[/tex]

(Б) [tex]\hspace{2em} \frac{5^{7}+3\cdot{5^{6}}}{(-125)^{2}}=\frac{{5^{1+6}}+3\cdot{5^{6}}}{125^{2}}=\frac{5^{1}\cdot{5^{6}}+3\cdot{5^{6}}}{(5^{3})^{2}}=\frac{5^{6}\cdot{(5+3)}}{5^{2\cdot{3}}}=\frac{5^{6}\cdot{8}}{5^{6}}=8[/tex]

(В) [tex]\hspace{2em} \frac{3^{-2}\cdot{2^{-3}}}{6^{-3}}=\frac{3^{1-3}\cdot{2^{-3}}}{6^{-3}}=\frac{3^{1}\cdot{3^{-3}}\cdot{2^{-3}}}{6^{-3}}=\frac{3\cdot(3\cdot{2})^{-3}}{6^{-3}}=\frac{3\cdot{6^{-3}}}{6^{-3}}=3[/tex]

(1) [tex]\hspace{1.2em} 5^{0}+\left(\frac{1}{7}\right)^{-1}=1+\left(\frac{7}{1}\right)^{1}=1+7=8[/tex]

(2) [tex]\hspace{1.2em} 2^{3}-(-3)^{2}-\left(\frac{1}{3}\right)^{-1}=8-(3^{2})-\left(\frac{3}{1}\right)^{1}=8-9-3=-4[/tex]

(3) [tex]\hspace{1.2em} 2^{3}-\frac{5^{7}}{25^{3}}=8-\frac{5^{7}}{(5^{2})^{3}}=8-\frac{5^{7}}{5^{6}}=8-5^{(7-6)}=8-5=3[/tex]

(4) [tex]\hspace{1.2em} 2^{-1}+2^{-1}=2\cdot{2^{-1}}=2\cdot{\left(\frac{1}{2^{1}}\right)}=2\cdot{\frac{1}{2}}=1[/tex]