Ответ: 1 - В , 2 - А , 3 - Г , 4 - Б .
Применяем свойства степеней .
[tex]\bf (a^{m})^{n}=a^{mn}\ \ ,\ \ a^{mn}=a^4\ \ \Rightarrow \ \ \ mn=4\\\\a^{m}\cdot a^{n}=a^{m+n}\ \ ,\ \ a^{m+n}=a^4\ \ \Rightarrow \ \ \ m+n=4\\\\\sqrt[8]{a^{m}}=a^{\frac{m}{8}}\ \ ,\ \ \sqrt{a^{n}}=a^{\frac{n}{2}}\ \ ,\ \ a^{\frac{m}{8}}=a^{\frac{n}{2}}\ \ \Rightarrow \ \ \ \dfrac{m}{8}=\dfrac{n}{2}\ \ ,\ \ m=4n\\\\\dfrac{a^{n}}{a^{m}}=a^{m-n}\ \ ,\ \ \dfrac{1}{a^4}=a^{-4}\ \ \Rightarrow \ \ a^{m-n}=a^{-4}\ \ ,\ \ m-n=-4\ ,\ \ n-m=4[/tex]
1) В
[tex](a {}^{m} ) {}^{n} = a{ }^{m n} = a {}^{4} \\ m n = 4[/tex]
2) А
[tex] {a}^{m} \times {a}^{n} = a {}^{m + n} = {a}^{4} \\ m + n = 4[/tex]
3) Г
[tex] \sqrt[8]{ {a}^{m} } = \sqrt{ {a}^{n} } \\ a {}^{ \frac{m}{8} } = {a}^{ \frac{n}{2} } \\ \frac{m}{8} = \frac{n}{2} \\ \frac{m}{4} = n \\ m = 4n[/tex]
4) Б
[tex] \frac{ {a}^{n} }{ {a}^{m} } = \frac{1}{ {a}^{4} } \\ {a}^{n - m} = {a}^{ - 4} \\ n - m = - 4 \\ m - n = 4[/tex]
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Ответ: 1 - В , 2 - А , 3 - Г , 4 - Б .
Применяем свойства степеней .
[tex]\bf (a^{m})^{n}=a^{mn}\ \ ,\ \ a^{mn}=a^4\ \ \Rightarrow \ \ \ mn=4\\\\a^{m}\cdot a^{n}=a^{m+n}\ \ ,\ \ a^{m+n}=a^4\ \ \Rightarrow \ \ \ m+n=4\\\\\sqrt[8]{a^{m}}=a^{\frac{m}{8}}\ \ ,\ \ \sqrt{a^{n}}=a^{\frac{n}{2}}\ \ ,\ \ a^{\frac{m}{8}}=a^{\frac{n}{2}}\ \ \Rightarrow \ \ \ \dfrac{m}{8}=\dfrac{n}{2}\ \ ,\ \ m=4n\\\\\dfrac{a^{n}}{a^{m}}=a^{m-n}\ \ ,\ \ \dfrac{1}{a^4}=a^{-4}\ \ \Rightarrow \ \ a^{m-n}=a^{-4}\ \ ,\ \ m-n=-4\ ,\ \ n-m=4[/tex]
1) В
[tex](a {}^{m} ) {}^{n} = a{ }^{m n} = a {}^{4} \\ m n = 4[/tex]
2) А
[tex] {a}^{m} \times {a}^{n} = a {}^{m + n} = {a}^{4} \\ m + n = 4[/tex]
3) Г
[tex] \sqrt[8]{ {a}^{m} } = \sqrt{ {a}^{n} } \\ a {}^{ \frac{m}{8} } = {a}^{ \frac{n}{2} } \\ \frac{m}{8} = \frac{n}{2} \\ \frac{m}{4} = n \\ m = 4n[/tex]
4) Б
[tex] \frac{ {a}^{n} }{ {a}^{m} } = \frac{1}{ {a}^{4} } \\ {a}^{n - m} = {a}^{ - 4} \\ n - m = - 4 \\ m - n = 4[/tex]