7.1–7.10. Найдите значение выражения: 7.1 \(\frac{a^{23}\cdot(b^5)^4}{(ab)^{20}},\ a=2,\ b=\sqrt2\); 7.2 \(\frac{a^{14}\cdot(b^6)^2}{(ab)^{12}},\ a=6,\ b=\sqrt6\); 7.3 \(\frac{a^{17}\cdot(b^5)^3}{(ab)^{15}},\ a=7,\ b=\sqrt7\); 7.4 \(\frac{a^{21}\cdot(b^9)^2}{(ab)^{18}},\ a=5,\ b=\sqrt5\); 7.5 \(\frac{a^{21}\cdot(b^6)^3}{(ab)^{18}},\ a=3,\ b=\sqrt3\); 7.6 \(\frac{a^{18}\cdot(b^8)^2}{(ab)^{16}},\ a=5,\ b=\sqrt5\); 7.7 \(\frac{a^{14}\cdot(b^4)^3}{(ab)^{12}},\ a=3,\ b=\sqrt3\); 7.8 \(\frac{a^{21}\cdot(b^4)^4}{(ab)^{16}},\ a=2,\ b=\sqrt2\); 7.9 \(\frac{a^{22}\cdot(b^3)^6}{(ab)^{18}},\ a=2,\ b=\sqrt2\); 7.10 \(\frac{a^{18}\cdot(b^7)^2}{(ab)^{14}},\ a=3,\ b=\sqrt3\).

Сокращаем степени отдельно для \(a\) и \(b\), используя \((ab)^n=a^nb^n\).

1. 7.1: \(a^3b^0=2^3=8\).
2. 7.2: \(a^2b^0=6^2=36\).
3. 7.3: \(a^2b^0=7^2=49\).
4. 7.4: \(a^3b^0=5^3=125\).
5. 7.5: \(a^3b^0=3^3=27\).
6. 7.6: \(a^2b^0=5^2=25\).
7. 7.7: \(a^2b^0=3^2=9\).
8. 7.8: \(a^5b^0=2^5=32\).
9. 7.9: \(a^4b^0=2^4=16\).
10. 7.10: \(a^4b^0=3^4=81\).

Ответ: 7.1) 8; 7.2) 36; 7.3) 49; 7.4) 125; 7.5) 27; 7.6) 25; 7.7) 9; 7.8) 32; 7.9) 16; 7.10) 81.