Toán Lớp 7: Tính nhanh :
\frac{2.6^9 -2^5 .18^4}{2^2 .6^8}
\frac{15^3 +5.15^2 -5^3}{18^3 +6.18^2 -6^3}
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Toán Lớp 7: Tính nhanh :
\frac{2.6^9 -2^5 .18^4}{2^2 .6^8}
\frac{15^3 +5.15^2 -5^3}{18^3 +6.18^2 -6^3}
Comments ( 2 )
= {2.2^9 .3^9 – 2^5 . 2^4 . 9^4 }/{2^2 . 2^8 . 3^8}
= {2^{10} . 3^9 – 2^9 . (3^2 )^4 }/{2^{10} . 3^8 }
= {2^{10} .3^9 – 2^9 . 3^8 }/{2^{10} . 3^8}
= {2^9 . 3^8 (2 . 3 -1)}/{2^{10} .3^8 }
= 5/2
= {5^3 .3^3 + 5.5^2 .3^2 – 5^3}/{6^3 . 3^3 + 6.6^2 . 3^2 – 6^3}
= {5^3 .3^3 + 5^3 .3^2 – 5^3}/{6^3 . 3^3 + 6^3 . 3^2 – 6^3}
= {5^3 (3^3 + 3^2 – 1)}/{6^3 (3^3 + 3^2 -1)}
= {5^3}/{6^3}
= {125}/{216}
=(2. (2.3)^9 – 2^5 .(2.9)⁴)/(2².(2.3)⁸)
=(2.2⁹ . 3⁹-2^5 . 2^4 . 9^4 )/(2² . 2⁸.3^8)
=(2^10 . 3^9 -2^9 . (3^2)⁴)/(2^10 . 3^8)
=(2^10 . 3^9 -2^9 . 3^8)/(2^10 .3^8)
=(2^9 . 3^8 (2.3-1))/(2^10 . 3^8)
=(2.3-1)/2
=5/2
b) (15³+5.15²-5³)/(18³+6.18²-6³)
=((3.5)³+5.(3.5)²-5³)/((6.3)³+6.(6.3)²-6³)
=(3³.5³+5.3².5²-5³)/(6³.3³+6.6².3²-6³)
=(3³.5³+5³.3²-5³)/(6³.3³+6³.3²-6³)
=(5³(3³+3²-1))/(6³(3³+3²-1))
=(5³)/(6³)
=125/216