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\(\textbf{Zdatak 1. }\) Izračunaj:

\(\textbf{a)  }\)  \(\left(\frac 23 x^2y^3\right)^2\);    \(\textbf{b)  }\)  \(\left(-\frac{1}{10} x^3y\right)^3\);    \(\textbf{a)  }\)  \(\left(4a^2y^7\right)^3\); 

\(\textbf{Zdatak 2. }\) Izračunaj: \[2\left(a^3\right)^4-5\left(a^2\right)^6+15a^12-3\left(a^4\right)^3\]

\(\textbf{Zdatak 3. }\) Izračunaj:

\(\textbf{a)  }\)  \(\left(\frac{2a^3}{5b^4}\right)^3\cdot\left(\frac {1}{10}a^2b^4\right)^2\);    \(\textbf{b)  }\)  \(\left(\frac{a^{-4}}{3b^{-2}}\right)^4\cdot\left(9a^2b^2\right)^3\); 

Zadaću napraviti za nedjelju,  24.5.2020.

Detalji

Hitova: 1557

	\(\mathbf{a)}\)		\((3\sqrt{2}+2\sqrt{3})^2\)		\(\mathbf{b)}\)		\((\sqrt{5}-2\sqrt{15})^2\)
	\(\mathbf{c)}\)		\((2\sqrt{3}-4\sqrt{5})^2\)		\(\mathbf{d)}\)		\((3\sqrt{6}+5\sqrt{3})^2\)
	\(\mathbf{e)}\)		\((1-\sqrt{3})^2(2+\sqrt{3})\)		\(\mathbf{a)}\)		\((1-\sqrt{2})^2(3+2\sqrt{2})\)

\(\mathbf{2.}\:\:\) Racionaliziraj nazivnik u razlomku: 

	\(\mathbf{a)}\)		\(\frac{1}{\sqrt{3}-\sqrt{2}}\)		\(\mathbf{b)}\)		\(\frac{1}{\sqrt{7}-\sqrt{6}}\)
	\(\mathbf{c)}\)		\(\frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}-\sqrt{5}}\)		\(\mathbf{d)}\)		\(\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\)
	\(\mathbf{e)}\)		\(\frac{2\sqrt{7}+7\sqrt{2}}{2\sqrt{7}-7\sqrt{2}}\)		\(\mathbf{a)}\)		\(\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\)

 

\(\mathbf{3.}\:\:\) Uradi naznačeno: 

\(\mathbf{a)}\) Izračunaj i rezultat djlimično korijenuj

	\(\mathbf{1)}\)		\(\sqrt{3}\cdot\sqrt[3]{9};\)		\(\mathbf{2)}\)		\(\sqrt{5}\cdot\sqrt[3]{625};\)
	\(\mathbf{3)}\)		\(\sqrt[3]{4}\cdot\sqrt[4]{48};\)		\(\mathbf{4)}\)		\(\sqrt{7}\cdot\sqrt[5]{49}\cdot\sqrt[4]{7};\)

 

\(\mathbf{b)}\) Pomnoži:

	\(\mathbf{1)}\)		\(\sqrt[5]{x}\cdot\sqrt[6]{x};\)		\(\mathbf{2)}\)		\(\sqrt[3]{a^2}\cdot\sqrt{a^3};\)
	\(\mathbf{3)}\)		\(\sqrt{a}\cdot\sqrt[3]{a}\cdot\sqrt[4]{a};\)		\(\mathbf{4)}\)		\(\sqrt{x}\cdot\sqrt[4]{x}\cdot\sqrt[8]{x};\)

 

\(\mathbf{4.}\:\:\) Izvedi naznačene operacije.

	\(\mathbf{a)}\)		\(\sqrt[5]{a^2}:\sqrt[4]{a};\)		\(\mathbf{b)}\)		\(\sqrt[5]{x^7y^6}:\sqrt[4]{y^2x^{-3}};\)
	\(\mathbf{c)}\)		\((\sqrt[3]{9}-2\sqrt{3})\cdot\sqrt[3]{3};\)		\(\mathbf{d)}\)		\((2\sqrt[6]{8}-\sqrt[4]{32}):\sqrt[4]{2};\)

 

\(\mathbf{5.}\:\:\) Svedi na potencije s racionalnim eksponentom i izračunaj: 

      

	\(\mathbf{a)}\)		\(\sqrt[4]{\frac{2}{3}a}\cdot \sqrt[6]{\frac{9}{4a}};\)		\(\mathbf{b)}\)		\(\sqrt[3]{a^4b^{-1}}\cdot \sqrt[4]{a^3b^2}\cdot\sqrt[6]{a^{-3}b^5};\)
	\(\mathbf{c)}\)		\(\sqrt[5]{a^7b^2}\cdot\sqrt{ab^3}:\sqrt[10]{a^{11}b^{-3}};\)		\(\mathbf{d)}\)		\(\sqrt{xy^7}:\sqrt[3]{x^5y}\cdot\sqrt[5]{x^5y};\)

\(\mathbf{6.}\:\:\) Odredi rješenja iracionalnih jednadžbi: 

	\(\mathbf{a)}\)		\(\sqrt{2x+1}=10;\)		\(\mathbf{b)}\)		\(2\sqrt{2x+2}-5=0;\)
	\(\mathbf{c)}\)		\(\sqrt{4+x}=2\sqrt{x-5};\)		\(\mathbf{d)}\)		\(\sqrt{5-x}=3\sqrt{x+1};\)
	\(\mathbf{e)}\)		\(\sqrt{x^2+x-2}=x;\)		\(\mathbf{a)}\)		\(\sqrt{x^2+5x+4}=x+2;\)

Detalji

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1. Obavi naznačene operacije s potencijam:

\( 1)\:\:3^{15}:3:3^{5} \)
\(  2)\:\:6^{21}:\left( 6^{12}\cdot 6^{7}\right) \)

\(  3)\:\:\left( \dfrac{2}{3}\right) ^{-6} \cdot \left[ \left( \dfrac{2}{3}\right) ^{5}:\left( \dfrac{2}{3}\right) ^{3}\right] \)

\(  4)\:\:4.3^{9}\cdot 4.3^{2} :4.3^{10} \)

\(  5)\:\:  2^{4}: \left( 2^{-4}\cdot 2^{5}\right) \)

\( 6)\:\:\left( \dfrac{7}{5}\right) ^{7}\cdot \left[ \left( \dfrac{7}{5}\right)^{5}:\left( \dfrac{7}{5}\right) ^{-3}\right]\)

 \( 7)\:\:ab^{5}\cdot b^{-3}c\cdot a^{2}b^{5}c^{-2}\)

2. Odredi vrijednost izraza za date vrijednosti nepoznanica

 \( a)\:\:4x^{2}+x^{3}y+5xy^{2}\:\:\:za\:\:\: x=2\:\:i\:\:y=-1 \)
  \( b)\:\:3xy^{2}-\dfrac{2}{3}xy-1\:\:\:za\:\:\: x=-3;y=-\dfrac{1}{3}\)