33.1. Представьте в виде квадрата одночлена заданные выражения: a) 4z², 9b⁴, 25m², 64p²; б) 16a²b⁴, 81x⁶y⁴, 49s²t⁸, 25k²t¹⁰; в) \(\frac{16}{25}\) p²s⁴t², \(\frac{9}{16}\) m⁴n¹², \(\frac{4}{49}\) a²b¹², \(\frac{25}{81}\) x⁴y⁸z¹⁶; г) 0,01a⁴b⁸, 0,04x⁶y⁶, 0,49k⁸t¹⁰, 1,21m⁶n⁴.

Ответ: a) \[(2z)^2, (3b^2)^2, (5m)^2, (8p)^2\]; б) \[(4ab^2)^2, (9x^3y^2)^2, (7st^4)^2, (5kt^5)^2\]; в) \[(\frac{4}{5}ps^2t)^2, (\frac{3}{4}m^2n^6)^2, (\frac{2}{7}ab^6)^2, (\frac{5}{9}x^2y^4z^8)^2\]; г) \[(0.1a^2b^4)^2, (0.2x^3y^3)^2, (0.7k^4t^5)^2, (1.1m^3n^2)^2\]

Решение: a) 4z² = (2z)², 9b⁴ = (3b²)², 25m² = (5m)², 64p² = (8p)² б) 16a²b⁴ = (4ab²)², 81x⁶y⁴ = (9x³y²)², 49s²t⁸ = (7st⁴)², 25k²t¹⁰ = (5kt⁵)² в) \(\frac{16}{25}\)p²s⁴t² = (\(\frac{4}{5}\)ps²t)², \(\frac{9}{16}\)m⁴n¹² = (\(\frac{3}{4}\)m²n⁶)², \(\frac{4}{49}\)a²b¹² = (\(\frac{2}{7}\)ab⁶)², \(\frac{25}{81}\)x⁴y⁸z¹⁶ = (\(\frac{5}{9}\)x²y⁴z⁸)² г) 0,01a⁴b⁸ = (0,1a²b⁴)², 0,04x⁶y⁶ = (0,2x³y³)² 0,49k⁸t¹⁰ = (0,7k⁴t⁵)², 1,21m⁶n⁴ = (1,1m³n²)²

Ответ: a) \[(2z)^2, (3b^2)^2, (5m)^2, (8p)^2\]; б) \[(4ab^2)^2, (9x^3y^2)^2, (7st^4)^2, (5kt^5)^2\]; в) \[(\frac{4}{5}ps^2t)^2, (\frac{3}{4}m^2n^6)^2, (\frac{2}{7}ab^6)^2, (\frac{5}{9}x^2y^4z^8)^2\]; г) \[(0.1a^2b^4)^2, (0.2x^3y^3)^2, (0.7k^4t^5)^2, (1.1m^3n^2)^2\]