1. .................=0
1) -0,25⁶ * 0,25⁻⁷= - 0,25⁶/0,25⁷ = - 1/0,25= - 4
2) 64^(1/3)=∛64=4
3) 3⁷ :3⁵=3²=9
4) 3⁰=1
5) -4-4+9-1=0
2. ......................=1/√a
1) ∛(а²√а)=∛(а² *а^(1/2))=∛1=1
2) ![\sqrt[4]{a \sqrt{a^{3}} } =a^{ \frac{1}{4} } * a^{ \frac{3}{8} } =a^{ \frac{5}{8} }](https://tex.z-dn.net/?f=+%5Csqrt%5B4%5D%7Ba+%5Csqrt%7Ba%5E%7B3%7D%7D+%7D+%3Da%5E%7B+%5Cfrac%7B1%7D%7B4%7D+%7D+%2A+a%5E%7B+%5Cfrac%7B3%7D%7B8%7D+%7D+%3Da%5E%7B+%5Cfrac%7B5%7D%7B8%7D+%7D+ "\sqrt[4]{a \sqrt{a^{3}} } =a^{ \frac{1}{4} } * a^{ \frac{3}{8} } =a^{ \frac{5}{8} }")
3) ![\frac{1}{a^{ \frac{5}{8} } } * \sqrt[8]{a} = a ^{ \frac{1}{8} } : a^{ \frac{5}{8} } = a^{- \frac{1}{2} } = \frac{1}{ \sqrt{a} }](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7Ba%5E%7B+%5Cfrac%7B5%7D%7B8%7D+%7D+%7D+%2A+%5Csqrt%5B8%5D%7Ba%7D+%3D+a+%5E%7B+%5Cfrac%7B1%7D%7B8%7D+%7D+%3A+a%5E%7B+%5Cfrac%7B5%7D%7B8%7D+%7D+%3D+a%5E%7B-+%5Cfrac%7B1%7D%7B2%7D+%7D+%3D+%5Cfrac%7B1%7D%7B+%5Csqrt%7Ba%7D+%7D+ "\frac{1}{a^{ \frac{5}{8} } } * \sqrt[8]{a} = a ^{ \frac{1}{8} } : a^{ \frac{5}{8} } = a^{- \frac{1}{2} } = \frac{1}{ \sqrt{a} }")
при а=64
1/√a=1/√64=1/8=0,125
3.
(3/5)^(0.5x)=4 17/27
(3/5)^(0.5x)=125/27
(3/5)^(0.5x)=(3/5)^(-3)
0.5x=-3
x= -6