`b, 15/60 + 12/19 + 2/9 - 10/8 + frac{-31}{19}`

  `= 1/4 + 12/19 + 2/9 - 5/4 + frac{-31}{19}`

  `= (1/4 - 5/4) + (12/19 + frac{-31}{19}) + 2/9`

  `= (1/4 + frac{-5}{4}) + frac{-19}{19} + 2/9`

  `= frac{-4}{4} + frac{-19}{19} + 2/9`

  `= -1 + (-1) + 2/9`

  `= -2 + 2/9`

  `= frac{-18}{9} + 2/9`

  `= frac{-16}{9}`

`c, frac{5^10 · 7^3 - 25^5 · 49^2}{(125 · 7)^3 + 5^9 · 7^3 · 8}`

  `= frac{5^10 · 7^3 - (5^2)^5 · (7^2)^2}{125^3 · 7^3 + 5^9 · 7^3 · 2^3}`

  `= frac{5^10 · 7^3 - 5^10 · 7^4}{(5^3)^3 · 7^3 + 5^9 · 14^3}`

  `= frac{5^10 · (7^3 - 7^4)}{5^9 · 7^3 + 5^9 · 14^3}`

  `= frac{5^10 · (7^3 · 1 - 7^3 · 7)}{5^9 · (7^3 + 14^3)}`

  `= frac{5^10 · 7^3 · (1 - 7)}{5^9 · (7^3 · 1 + 7^3 · 2^3)}`

  `= frac{5^10 · 7^3 · (1 - 7)}{5^9 · 7^3 · (1 + 2^3)}`

  `= frac{5 · (1 - 7)}{1 + 2^3}`

  `= frac{5 · (-6)}{1 + 8}`

  `= frac{-30}{9} = frac{-10}{3}`

Đáp án:

a) $\dfrac{16}{49}$ 

b) $\dfrac{-16}9$

c) $\dfrac{-10}3$

Giải thích các bước giải:

$a)\,\left(\dfrac{-4}7\right)^{\large25}:\left(\dfrac{-4}7\right)^{\large23}\\=\left(\dfrac{-4}7\right)^{\large2}=\dfrac{16}{49}\\b)\,\dfrac{15}{60}+\dfrac{12}{19}+\dfrac29-\dfrac{10}8=\dfrac{-31}{19}\\=\dfrac{1-4}4+\dfrac{12-31}{19}+\dfrac29\\=-1+(-1)+\dfrac29\\=\dfrac{-16}9\\c)\,\dfrac{5^{10}.7^3-25^5.49^2}{(125.7)^2+5^9.7^3.8}\\=\dfrac{5^{10}.7^3-\left(5^2\right)^5.\!\left(7^2\right)^2}{\left(5^3.7\right)^3+5^9.7^3.8}\\=\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.7^3.8}\\=\dfrac{5^9.7^3.(5-5.7)}{5^9.7^3.(1+8)}\\=\dfrac{5-5.7}{1+8}\\=\dfrac{-10}3$