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Viết các tích sau thành dạng lũy thừa của một số nguyên:
a) \({\rm{}}\left( { – 8} \right).{\left( { – 3} \right)^3}.\left( { + 125} \right)\)
b) \(27.{\left( { – 2} \right)^3}.\left( { – 7} \right).\left( { + 49} \right)\)
a) \({\rm{}}\left( { – 8} \right).{\left( { – 3} \right)^3}.\left( { + 125} \right)\)
= \(\left[ {\left( { – 2} \right).\left( { – 2} \right).\left( { – 2} \right)} \right].\left[ {\left( { – 3} \right).\left( { – 3} \right).\left( { – 3} \right)} \right].\left( {5.5.5} \right)\)
= \(\left[ {\left( { – 2} \right).\left( { – 3} \right).5} \right].\left[ {\left( { – 2} \right).\left( { – 3} \right).5} \right].\left[ {\left( { – 2} \right).\left( { – 3} \right).5} \right] \)
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= \(30.30.30 = {30^3}\)
b) \(27.{\left( { – 2} \right)^3}.\left( { – 7} \right).\left( { + 49} \right) \)
= \(\left( {3.3.3} \right).\left[ {\left( { – 2} \right).\left( { – 2} \right).\left( { – 2} \right)} \right].\left[ {\left( { – 7} \right).\left( { – 7} \right).\left( { – 7} \right)} \right]\)
= \(\left[ {3.\left( { – 2} \right).\left( { – 7} \right)} \right].\left[ {3.\left( { – 2} \right).\left( { – 7} \right)} \right].\left[ {3.\left( { – 2} \right).\left( { – 7} \right)} \right]\)
= \(42.42.42 = {42^3}\)