Answer:
Step-by-step explanation:
[tex]\dfrac{(2*3^{-2})^{3}(5*3^{2})^{2}}{3^{-2}*(5*2)^{2}}=\dfrac{2^{3}*3^{-2*3}*5^{2}*3^{2*2}}{3^{-2}*5^{2}*2^{2}}\\\\\\=\dfrac{2^{3}*3^{-6}*5^{2}*3^{4}}{3^{-2}*5^{2}*2^{2}}\\\\\\=2^{3-2}*3^{-6+4-(-2)}*5^{2-2} = 2^{1}*3^{-6+4+2}*5^{0}\\\\\\=2*3^{0}*5^{0}=2*1*1 \\\\\\= 2[/tex]
[tex]3) 3^{3}(4^{0})^{2}*(3*2)^{-3} * 2^{2}=3^{3} *1 *3^{-3}*2^{-3}*2^{2}\\\\\\= 3^{3-3}*2^{-3+2} = 3^{0}*2^{-1} = 1*2^{-1}\\\\\\=\dfrac{1}{2}[/tex]
[tex]3)\dfrac{3^{7}*4^{7}*(2*5)^{-3}*5^{2}}{12^{7}*5^{-1}*2^{-4}}\\\\\\=\dfrac{3^{7}*((2^{2})^{7}*2^{-3}*5^{-3}*5^{2}}{(2^{2}*3)^{7}*5^{-1}*2^{-4}}\\\\\\=\dfrac{3^{7}*2^{2*7}*2^{-3}*5^{-3}*5^{2}}{2^{2*7}*3^{7}*5^{-1}*2^{-4}}\\\\\\=\dfrac{3^{7}*2^{14}*2^{-3}*5^{-3}*5^{2}}{2^{14}*3^{7}*5^{-1}*2^{-4}}\\\\\\=3^{7-7}*2^{14-3-14+4}*5^{-3+2+1}\\\\=3^{0}*2^{1}*5^{0}\\\\\\=1*2*1\\\\\\=2[/tex]
Hint:
[tex]a^{0}=1\\\\\dfrac{a^{m}}{a^{n}}=a^{m-n}\\\\\\a^{m}*a^{n}=a^{m+n}\\\\\\a^{-m}=\dfrac{1}{a^{m}}[/tex]
