10 клас. Алгебра. Урок 21. Перетворення виразів, які містять степені з раціональним показником

1) $a^{\frac12}b^{\frac12}\left(a^{\frac12}+b^{\frac12}\right);$

9) $\left(b^{0,4}+3\right)^2-6b^{0,4};$

2) $2a^{\frac12}\left(a^{\frac12}-4\right)+8a^{\frac12};$

10) $\left(c^{\frac13}-1\right)\left(c^{\frac23}+c^{\frac13}+1\right);$

3)$\left(a^{0,5}-6b^{0,3}\right)\left(2a^{0,5}+b^{0,3}\right);$

11) $\left(a^{\frac13}+a^{\frac12}\right)\left(a^{\frac23}-a^{\frac56}+a\right);$

4) $\left(m^{\frac14}-n^{\frac14}\right)\left(m^{\frac14}+n^{\frac14}\right);$

12) $a^{\frac16}\left(a^{\frac16}+10\right)-\left(a^{\frac16}+5\right)^2;$

5) $\left(3b^{\frac23}-c^{\frac32}\right)\left(3b^{\frac23}+c^{\frac32}\right);$

13) $\left(b^{\frac35}-2b^{\frac13}\right)^2+4b^{\frac16}\left(b^{\frac{23}{30}}-b^{\frac12}\right);$

6) $\left(a^{\frac13}+b^{\frac13}\right)^2;$

14) $\left(a^{\frac16}+b^{\frac16}\right)\left(a^{\frac16}-b^{\frac16}\right)\left(a^{\frac13}-b^{\frac13}\right);$

7) $\left(4n^{-\frac56}+3n^{\frac56}\right)^2;$

15) $\left(x^{\frac29}-1\right)\left(x^{\frac49}+x^{\frac29}+1\right)\left(x^{\frac23}+1\right).$

8) $\left(a^{-\frac12}-\frac14a^{-\frac16}\right)^2;$

1) $a+3a^{\frac12};$

5) $m^{\frac35}-m^{\frac15};$

2) $b^{\frac12}-4b^{\frac14};$

6) $6^{\frac14}-3^{\frac14};$

3) $ab^{\frac13}-a^{\frac13}b;$

7) $2-2^{\frac17};$

4) $c^{\frac34}-c^{\frac12};$

8) $x^{\frac56}+x^{\frac13}.$

1) $\frac{a-5a^{\frac12}}{a^{\frac12}-5};$

5) $\frac{a-b}{ab^{\frac12}+a^{\frac12}b};$

9) $\frac{m^{\frac12}-n^{\frac12}}{m^{\frac32}-n^{\frac32}};$

2) $\frac{a^{\frac23}}{a^{\frac53}+a^{\frac23}};$

6) $\frac{a+2a^{\frac12}b^{\frac12}+b}{a^{\frac12}+b^{\frac12}};$

10) $\frac{x-6x^{\frac16}}{x^{\frac76}-6x^{\frac13}};$

3) $\frac{b^{\frac34}+b^{\frac12}c^{\frac14}}{b^{\frac14}+c^{\frac14}};$

7) $\frac{4c^{\frac23}-12c^{\frac13}d^{\frac13}+9d^{\frac23}}{2c^{\frac13}-3d^{\frac13}};$

11) $\frac{a^{\frac34}+7a^{\frac12}}{a-49a^{\frac12}};$

4) $\frac{a-4b}{a^{0,5}+2b^{0,5}};$

8) $\frac{a+b}{a^{\frac13}+b^{\frac13}};$

12) $\frac{30^{\frac15}-6^{\frac15}}{10^{\frac15}-2^{\frac15}}.$