Phương pháp giải:

Tính nhẩm các số rồi điền kết quả vào chỗ trống.

Lời giải chi tiết:

Tính nhẩm:

\(\dfrac{4^{10}.9^6+3^{12}.8^5}{6^{13}.4-2^{16}.3^{12}}\)

\(=\dfrac{\left(2^2\right)^{10}.\left(3^2\right)^6+3^{12}.\left(2^3\right)^5}{\left(2.3\right)^{13}.2^2-2^{16}.3^{12}}\)

\(=\dfrac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{13}.3^{13}.2^2-2^{16}.3^{12}}\)

\(=\dfrac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{15}.3^{13}-2^{16}.3^{12}}\)

\(=\dfrac{2^{15}.3^{12}.\left(2^5+1\right)}{2^{15}.3^{13}.\left(3-2\right)}\)

\(=\dfrac{2^5+1}{3-2}\)

\(=\dfrac{32+1}{1}=33\)

a: =6/12*7/14*8/16*9/18=1/2*1/2*1/2*1/2=1/16

b: =4/12*15/3*9/25*24/8

=1/3*3*5*9/25=9/5

Phương pháp giải:

Trừ nhẩm các số rồi điền kết quả vào chỗ trống.

Lời giải chi tiết:

18 − 9 = 9           17 − 9 = 8

16 − 9 = 7           15 − 6 = 9

15 − 7 = 8           15 − 8 = 7

11 − 7 = 4           12 − 8 = 4

13 − 9 = 4           11 − 6 = 5

14 − 6 = 8           11 − 3 = 8

18-9=9;  17-9=8;  16-9=7;  15-6=9;  15-7=8;  15-8=7.

\(\frac{4^{10}.9^6+3^{12}.8^5}{6^{13}.4-2^{16}.3^{12}}\)

\(=\frac{\left(2^2\right)^{10}.\left(3^2\right)^6+3^{12}.\left(2^3\right)^5}{\left(2.3\right)^{13}.2^2-2^{16}.3^{12}}\)

\(=\frac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{13}.3^{13}.2^2-2^{16}.3^{12}}\)

\(=\frac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{15}.3^{12}.3-3^{12}.2^{16}}\)

\(=\frac{2^4}{3}\)

3653/224

\(\dfrac{5}{15}+\dfrac{48}{16}=\dfrac{1}{3}+3=\dfrac{1}{3}+\dfrac{9}{3}=\dfrac{10}{3}\)

\(\dfrac{6}{9}:\dfrac{12}{36}=\dfrac{2}{3}:\dfrac{1}{3}=\dfrac{2}{3}\times\dfrac{3}{1}=\dfrac{6}{3}=2\)

\(\dfrac{4}{12}\times\dfrac{56}{14}=\dfrac{1}{3}\times4=\dfrac{4}{3}\)