5.6. Ықшамдаңдар: 1) (a · b)³/b²; 2) (x/y)⁵ · y⁷; 3) (d · t)⁹/d⁷; 4) (x · y)⁶/x⁵; 5) (a · c)¹⁰/c⁸; 6) m¹² · (n/m)¹⁰; 7) (x⁵y⁶)⁴/(x²⁰y²²); 8) (a⁴/b³)⁵ · b¹⁷; 9) (x⁸y⁴)³/(x²³y¹²).

Қолданылатын қасиеттер: \((ab)^n=a^nb^n\), \(a^m:a^n=a^{m-n}\), \(a^m\cdot a^n=a^{m+n}\).

1. \(\frac{(ab)^3}{b^2}=\frac{a^3b^3}{b^2}=a^3b\).
2. \(\left(\frac{x}{y}\right)^5y^7=\frac{x^5}{y^5}y^7=x^5y^2\).
3. \(\frac{(dt)^9}{d^7}=\frac{d^9t^9}{d^7}=d^2t^9\).
4. \(\frac{(xy)^6}{x^5}=\frac{x^6y^6}{x^5}=xy^6\).
5. \(\frac{(ac)^{10}}{c^8}=\frac{a^{10}c^{10}}{c^8}=a^{10}c^2\).
6. \(m^{12}\left(\frac{n}{m}\right)^{10}=m^{12}\frac{n^{10}}{m^{10}}=m^2n^{10}\).
7. \(\frac{(x^5y^6)^4}{x^{20}y^{22}}=\frac{x^{20}y^{24}}{x^{20}y^{22}}=y^2\).
8. \(\left(\frac{a^4}{b^3}\right)^5b^{17}=\frac{a^{20}}{b^{15}}b^{17}=a^{20}b^2\).
9. \(\frac{(x^8y^4)^3}{x^{23}y^{12}}=\frac{x^{24}y^{12}}{x^{23}y^{12}}=x\).

Жауабы: 1) a³b; 2) x⁵y²; 3) d²t⁹; 4) xy⁶; 5) a¹⁰c²; 6) m²n¹⁰; 7) y²; 8) a²⁰b²; 9) x.