3. Упростите: a) $(-5xy^3)^2 \cdot (2xy^2z)^2$; б) $10000 \cdot (-(0,1a^4b^5)^3)^2$; в) $(\frac{-1}{3}a^3y)^2 \cdot 3ab$.

a) $(-5xy^3)^2 \cdot (2xy^2z)^2 = (-5)^2x^2(y^3)^2 \cdot 2^2x^2(y^2)^2z^2 = 25x^2y^6 \cdot 4x^2y^4z^2 = 25 \cdot 4 \cdot x^2 \cdot x^2 \cdot y^6 \cdot y^4 \cdot z^2 = 100x^4y^{10}z^2$. б) $10000 \cdot (-(0,1a^4b^5)^3)^2 = 10000 \cdot (-(0,1)^3(a^4)^3(b^5)^3)^2 = 10000 \cdot (-0,001a^{12}b^{15})^2 = 10000 \cdot (0,001)^2(a^{12})^2(b^{15})^2 = 10000 \cdot 0,000001a^{24}b^{30} = 0,01a^{24}b^{30}$. в) $(\frac{-1}{3}a^3y)^2 \cdot 3ab = (\frac{-1}{3})^2(a^3)^2y^2 \cdot 3ab = \frac{1}{9}a^6y^2 \cdot 3ab = \frac{1}{9} \cdot 3 \cdot a^6 \cdot a \cdot y^2 \cdot b = \frac{1}{3}a^7by^2$. Ответ: a) $100x^4y^{10}z^2$; б) $0,01a^{24}b^{30}$; в) $\frac{1}{3}a^7by^2$.