Упр.37.19 ГДЗ Мордкович 10-11 класс (Алгебра)
- а) $$\left(a^{0{,}4}\right)^{\frac{1}{2}}\cdot a^{0{,}8}$$;
- б) $$\sqrt[10]{c}\cdot\left(c^{-1{,}2}\right)^{\frac{3}{4}}$$;
- в) $$\left(x^{\frac{3}{4}}\right)^{\frac{5}{4}}\cdot\left(\sqrt[4]{x}\right)^{\frac{17}{4}}$$;
- г) $$\left(b^{0{,}8}\right)^{-\frac{3}{4}}\cdot\left(b^{-\frac{2}{5}}\right)^{-1{,}5}$$.
а) $$\left(a^{0,4}\right)^{\frac12}\cdot a^{0,8}= \left(a^{\frac25}\right)^{\frac12}\cdot a^{\frac45}=a^{\frac25\cdot\frac12}\cdot a^{\frac45}=a^{\frac15+\frac45}=a^1=a.$$
Ответ: $$a$$
б) $$\sqrt[10]{c}\cdot \left(c^{-1,2}\right)^{\frac34}=c^{\frac1{10}}\cdot \left(c^{-\frac65}\right)^{\frac34}=c^{\frac1{10}}\cdot c^{-\frac65\cdot\frac34}=c^{\frac1{10}}\cdot c^{-\frac9{10}}=c^{-\frac45}=\frac1{\sqrt[5]{c^4}}.$$
Ответ: $$\frac1{\sqrt[5]{c^4}}$$
в) $$\left(x^{\frac34}\right)^{\frac54}\cdot \left(\sqrt[4]{x}\right)^{\frac{17}{4}}=\left(x^{\frac34}\right)^{\frac54}\cdot \left(x^{\frac14}\right)^{\frac{17}{4}}=x^{\frac34\cdot\frac54}\cdot x^{\frac14\cdot\frac{17}{4}}=x^{\frac{15}{16}+\frac{17}{16}}=x^2.$$
Ответ: $$x^2$$
г) $$\left(b^{0,8}\right)^{-\frac34}\cdot \left(b^{-\frac25}\right)^{-1,5}=\left(b^{\frac45}\right)^{-\frac34}\cdot \left(b^{-\frac25}\right)^{-\frac32}=b^{\frac45\cdot\left(-\frac34\right)}\cdot b^{-\frac25\cdot\left(-\frac32\right)}=b^{-\,\frac35}\cdot b^{\frac35}=b^0=1.$$
Ответ: $$1$$
