68. Выполните возведение в степень: 1) (5a³b²)²; 2) (-4x²y⁴)²; 3) (-2x²yz³)³; 4) (1/2 m³n⁴)²; 5) (9x⁴y²z⁶)²; 6) (1 1/2 a³b¹²)².

• 1) $$(5a^3b^2)^2 = 5^2 \cdot (a^3)^2 \cdot (b^2)^2 = 25a^6b^4$$.
• 2) $$(-4x^2y^4)^2 = (-4)^2 \cdot (x^2)^2 \cdot (y^4)^2 = 16x^4y^8$$.
• 3) $$(-2x^2yz^3)^3 = (-2)^3 \cdot (x^2)^3 \cdot y^3 \cdot (z^3)^3 = -8x^6y^3z^9$$.
• 4) $$\left(\frac{1}{2}m^3n^4\right)^2 = \left(\frac{1}{2}\right)^2 \cdot (m^3)^2 \cdot (n^4)^2 = \frac{1}{4}m^6n^8$$.
• 5) $$(9x^4y^2z^6)^2 = 9^2 \cdot (x^4)^2 \cdot (y^2)^2 \cdot (z^6)^2 = 81x^8y^4z^{12}$$.
• 6) $$\left(1\frac{1}{2}a^3b^{12}\right)^2 = \left(\frac{3}{2}a^3b^{12}\right)^2 = \left(\frac{3}{2}\right)^2 \cdot (a^3)^2 \cdot (b^{12})^2 = \frac{9}{4}a^6b^{24} = 2\frac{1}{4}a^6b^{24}$$.

Ответ:

• 1) $$25a^6b^4$$
• 2) $$16x^4y^8$$
• 3) $$-8x^6y^3z^9$$
• 4) $$\frac{1}{4}m^6n^8$$
• 5) $$81x^8y^4z^{12}$$
• 6) $$2\frac{1}{4}a^6b^{24}$$