Question

scrieti ca fiind patratul unui numar intreg a) 5⁴× 9³× (-2)⁸= b) [(-7)³]²× (-1)¹²×(-16)³ = c) (-9)⁵×(-2) ⁴ × (-3)⁶ d) 16³×(-25) × (-49)³​

Answer 1

${5}^{4} \times ( {3}^{2})^{3} \times ( - 1)^{8} \times {2}^{8} = {5}^{4} \times {3}^{6} \times {2}^{8} = ( {5}^{2} )^{2} \times ( {3}^{3} ) ^{2} \times ( {2}^{4}) ^{2} = ( {5}^{2} \times {3}^{3} \times {2}^{4} )^{2} = 10800 ^{2}$

${( - 7)}^{6} \times {( - 1)}^{3} \times {16}^{3} = {( - 1)}^{6} \times {7}^{6} \times ( - 1) \times {2}^{12} = -{ ({7}^{3}) }^{2} \times {(2^{6} )}^{2} = -( {7}^{3} \times {2}^{6} ) ^{2} = -{21952}^{2}$

${( - 1)}^{5} \times {9}^{5} \times {( - 1)}^{4} \times {2}^{4} \times {( - 1)}^{6} \times {3}^{6} = -({3}^{5}) ^{2} \times { ({2}^{2})}^{2} \times ({3}^{3})^{2} = -{( {3}^{8} \times {2}^{2} )}^{2} = -{26244}^{2}$

${({2}^{4})}^{3}\times(-1)\times{5}^{2}\times{(-1)^{3}}\times{({7}^{2})}^{3}={({2}^{6})}^{2}\times{5}^{2}\times{({7}^{3})}^{2}={({2}^{6} \times5\times{7}^{3})}^{2}= {109760}^{2}$