Question

помогите ,алгебра! н.6.12​

Answer 1

Ответ:

Применяем свойства степеней:   $\bf a^{-1}=\dfrac{1}{a}\ \ ,\ \ a^{-n}=\dfrac{1}{a^{n}}\ \ ,$  

                                                        $\bf (a^{n})^{k}=a^{n\cdot k}\ \ ,\ \ (a\cdot b)^{k}=a^{k}\cdot b^{k}\ \ ,\ \ a^{n}\cdot a^{k}=a^{n+k}$   .

$1)\ \ \Big(343^{\frac{1}{2}}\cdot \Big(\dfrac{1}{49}\Big)^{\frac{3}{8}}\Big)^{\frac{4}{3}}=\Big((7^3)^{^{\frac{1}{2}}}\cdot (7^{-2})^{^{\frac{3}{8}}}\Big)^{\frac{4}{3}}=\Big(7^{^{\frac{3}{2}}}\cdot 7^{^{-\frac{3}{4}}}\Big)^{\frac{4}{3}}=\Big(7^{^{\frac{3}{4}}}\Big)^{\frac{4}{3}}=7^{^{1}}=7$

$2)\ \ 10^{^{\frac{1}{4}}}\cdot 40^{^{\frac{1}{4}}}\cdot 5^{^{\frac{1}{2}}}=(5\cdot 2)^{^{\frac{1}4}}}\cdot (2^3\cdot 5)^{^{\frac{1}{4}}}\cdot 5^{^{\frac{1}{2}}}=5^{^{\frac{1}{4}}}\cdot 2^{^{\frac{1}{4}}}\cdot 2^{^{\frac{3}{4}}}\cdot 5^{^{\frac{1}{4}}}\cdot 5^{^{\frac{1}{2}}}=\\\\=5^{^{\frac{1}{4}+\frac{1}{4}+\frac{1}{2}}}\cdot 2^{^{\frac{1}{4}+\frac{3}{4}}}=5^1\cdot 2^1=10$

$3)\ \ 0,0016^{^{-\frac{3}{4}}}-0,04^{^{-\frac{1}{2}}}+0,216^{^{-\frac{2}{3}}}=\Big((0,2)^4\Big)^{-\frac{3}{4}}-\Big((0,2)^2\Big)^{-\frac{1}{2}}+\Big((0,6)^3\Big)^{-\frac{2}{3}}=\\\\=\Big(0,2\Big)^{-3}-\Big(0,2\Big)^{-1}+\Big(0,6\Big)^{-2}=\Big(\dfrac{1}{5}\Big)^{-3}-\Big(\dfrac{1}{5}\Big)^{-1}+\Big(\dfrac{1}{5}\cdot 3\Big)^{-2}=\\\\=5^3-5^1+5^2\cdot \dfrac{1}{3^2}=125-5+\dfrac{25}{9}=120+\dfrac{25}{9}=120+2\dfrac{7}{9}=122\dfrac{7}{9}$

$4)\ \ 625^{-1,25}\ \cdot \ 25^{1,5}\ \cdot \ 125^{^{\frac{2}{3}}}=(5^4)^{^{-\frac{5}{4}}}\cdot (5^2)^{^{\frac{3}{2}}}\cdot (5^3)^{^{\frac{2}{3}}}=5^{-5}\cdot 5^{3}\cdot 5^{2}=\\\\=5^{-5+3+2}=5^0=1$

Answer 2

Ответ:

Объяснение:

1) (343^(1/2) ·(1/49)^(3/8))^(4/3)=(7^(3·1/2) ·7^(-2·3/8))^(4/3)=(7^(6/4 -3/4))^(4/3)=7^(3/4 ·4/3)=7^(3/3)=7

2) 10^(1/4) ·40^(1/4) ·5^(1/2)=5^(1/4) ·2^(1/4) ·5^(1/4) ·2^(3·1/4) ·5^(1/2)=5^(1/4 +1/4 +2/4) ·2^(1/4 +3/4)=5¹·2¹=10

3) 0,0016^(-3/4) -0,04^(-1/2) +0,216^(-2/3)=(10⁴/2⁴)^(3/4) -(10²/2²)^(1/2) +(10³/6³)((2/3)=10^(4·3/4) ·2^(-4·3/4) -10^(2·1/2) ·2^(-2·1/2) +10^(3·2/3) ·6^(-3·2/3)=10³·2⁻³-10¹·2⁻¹+10²·6⁻²=1000/8 -10/2 +100/36=125-5 +2 7/9=122 7/9

4) 625^(-1,25) ·25^(1,5) ·125^(2/3)=5^(4·(-5/4)) ·5^(2·1,5) ·5^(3·2/3)=5⁵⁺³⁺²=5¹⁰