Toán Lớp 6: 1, rút gọn biểu thức
a, A= 4^6 x 9^5+ 6^9 x 120 / 8^4 x 3^12
b,B= 5.4^15.9^9-4.3^26.8^9 / 7. 2^29 .27^6 -5. 2^29 . 9^16
c,C= 5^10 .7^3 -25^3.49^2 / ( 125.7)^3+ 5^9 .14^2
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Toán Lớp 6: 1, rút gọn biểu thức
a, A= 4^6 x 9^5+ 6^9 x 120 / 8^4 x 3^12
b,B= 5.4^15.9^9-4.3^26.8^9 / 7. 2^29 .27^6 -5. 2^29 . 9^16
c,C= 5^10 .7^3 -25^3.49^2 / ( 125.7)^3+ 5^9 .14^2
Comments ( 2 )
= frac{(2^2)^6 · (3^2)^5+ 2^9 ·3^9· 120}{(2^3)^4 · 3^12}
= frac{2^12 · 3^10+ 2^9 ·3^9· 2^3·3·5}{2^12 · 3^12}
= frac{2^12 · 3^10+ 2^12 ·3^10·5}{2^12 · 3^12}
= frac{2^12·3^10(1+5)}{2^12 · 3^12}
= frac{2^12·3^10·6}{2^12 · 3^12}
= frac{2^12·3^10·2·3}{2^12 · 3^12}
= frac{2^13·3^11}{2^12 · 3^12}
= 2/3
b) B = frac{5 · 4^15 · 9^9 – 4 ·3^26 ·8^9}{7· 2^29 ·27^6 – 5· 2^29 · 9^16}
=frac{5 · (2^2)^15 · (3^2)^9 – 4 ·3^26 ·(2^3)^9}{5· 2^29 · 9^16-7· 2^29 ·27^6}
=frac{5 · (2^2)^15 · (3^2)^9 – 2^2 · 3^26 ·(2^3)^9}{5 · 2^29 · (3^2)^16-7· 2^29 · (3^3)^6}
=frac{5 · 2^30 · 3^18 – 2^2 · 3^26 · 2^27}{5 · 2^29 · 3^32-7· 2^29 · 3^18 }
=frac{5 · 2^30 · 3^18 – 3^26 · 2^29}{5 · 2^29 · 3^32-7 · 2^29 · 3^18}
=frac{3^26 · 2^29-5 · 2^30 · 3^18}{5 · 2^29 · 3^32-7 · 2^29 · 3^18}
=frac{2^29 · 3^18 (3^8-5 · 2)}{2^29 · 3^18(5 · 3^14 – 7)}
=frac{3^8-5 · 2}{5 · 3^14}
c) C=frac{ 5^10 ·7^3 -25^3·49^2}{( 125·7)^3+ 5^9 ·14^2}
=frac{ 5^10 ·7^3 -(5^2)^3·(7^2)^2}{5^9 · 7^3+ 5^9 ·2^2·7^2}
=frac{ 5^10 ·7^3 -5^6·7^4}{5^9 · 7^3+ 5^9 ·2^2·7^2}
=frac{ 5^6 ·7^3(5^4-7)}{5^9 · 7^2(7+2^2)}
=frac{7^2(5^4-7)}{5^3 (7+2^2)}