\(5^8:25^2=5^8:5^4\)

=5⁴=625

\(4^9:64^2=4^9:\left(2^2\right)^6\)

=4⁹:4⁶

=4³=64

a.

A = 72^3.54^2/108^4

A = (72.54:108)^2:108^2.72

A = 36^2:108^2.72

A = (36:108)^2.72

A = (1/3)^2.72

A = 72/9

A = 8

B = \(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)

B = \(\frac{3^{10}.\left(11+5\right)}{3^9.2^4}\)

B = \(\frac{3^{10}.16}{3^9.16}\)

B = 3

a, \(A=\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}=\dfrac{3^{10}.\left(11+5\right)}{3^9.2^4}\)

\(=\dfrac{3^{10}.2^4}{3^9.2^4}=3\)

b, \(B=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}=\dfrac{2^{10}.78}{2^8.104}\)

\(=\dfrac{2^2.3}{4}=3\)

c, \(C=\dfrac{4^9.36+64^4}{16^4.100}=\dfrac{\left(2^2\right)^9.36+\left(2^6\right)^4}{\left(2^4\right)^4.100}\)

\(=\dfrac{2^{18}.36+2^{24}}{2^{16}.100}=\dfrac{2^{18}.\left(36+2^6\right)}{2^{16}.100}\)

\(=\dfrac{2^4.100}{100}=2^4=16\)

Câu d làm tương tự! Chúc bạn học tốt!!!

d, \(D=\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}\)

\(=\dfrac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=2^3=8\)

Chúc bạn học tốt!!!

a) $3^8:3^6=3^{8-6}=3^2$

$19^7:19^3=19^{7-3}=19^4$

$2^{10}:8^3=2^{10}:(2^3)^3=2^{10}:2^9=2^{10-9}=2^1$

$12^7:6^7=(12:6)^7=2^7$

$27^5:81^3=(3^3)^5:(3^4)^3=3^{15}:3^{12}=3^{15-12}=3^3$

b) $10^6:10=10^{6-1}=10^5$

$5^8:25^2=5^8:(5^2)^2=5^8:5^4=5^{8-4}=5^4$

$4^9:64^2=4^9:(4^3)^2=4^9:4^6=4^{9-6}=4^3$

$2^25:32^4=2^{25}:(2^5)^4=2^{25}:2^{20}=2^{25-20}=2^5$

$18^3:9^3=(18:9)^3=2^3$

\(\cdot3^8:3^6=3^{8-6}=3^2\)

\(\cdot19^7:19^3=19^{7-3}=19^4\)

\(\cdot2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^9=2\)

\(\cdot12^7:6^7=\left(12:6\right)^7=2^7\)

\(\cdot27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)

\(\cdot10^6:10=10^{6-1}=10^5\)

\(\cdot5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^4=5^4\)

\(\cdot4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^6=4^3\)

\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^5\)

\(18^3:9^3=\left(18:9\right)^3=2^3\)

Câu b:

B = (3\(^{10}\).11 + 3\(^{10}\).5) : (3\(^9\).2\(^4\))

B = 3\(^{10}\).(11 + 5): (3\(^9\).2\(^4\))

B = 3\(^{10}\).16:(3\(^9\).2\(^4\))

B = (3\(^{10}\) : 3\(^9\)).(16 : 2\(^4\))

B = 3.1

B = 3

Câu c:

C = (2\(^{10}\).13 + 2\(^{10}\).65) : (2\(^8\).104)

C = 2\(^{10}\).(13 + 65):(2\(^8\).104)

C = 2\(^{10}\).78 : (2\(^8\).104)

C = (2\(^{10}\) : 2\(^8\)).(78 : 104)

C = 2\(^2\).\(\frac34\)

C = 3

a) \(4^{10}.2^{30}=\left(2^2\right)^{10}.2^{30}=2^{2.10}.2^{30}=2^{20}.2^{30}=2^{20+30}=2^{50}\)

b) \(9^{25}.27^4.81^3=\left(3^2\right)^{25}.\left(3^3\right)^4.\left(3^4\right)^3=3^{3.25}.3^{3.4}.3^{4.3}=3^{75}.3^{12}.3^{12}=3^{75+12+12}=3^{99}\)

c) \(25^{50}.125^5=\left(5^2\right)^{50}.\left(5^3\right)^5=5^{2.50}.5^{3.5}=5^{100}.5^{15}=5^{100+15}=5^{115}\)

d) \(64^3.4^8.16^4=\left(4^3\right)^3.4^8.\left(4^2\right)^4=4^{3.3}.4^8.4^{2.4}=4^9.4^8.4^8=4^{9+8+8}=4^{25}\)

e) \(3^8:3^6=3^{8-6}=3^2\)

f)  \(2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^{3.3}=2^{10}:2^9=2^{10-9}=2\)

g) \(12^7:6^7=\left(12:6\right)^7=2^7\)

h_ \(21^5:81^3\)kết quả là số dư nên không tính ( đề sai )

mòi tay không

Học thì sao phải mỏi tay

a,71.2-6.(2x+5)=10^5:10^3                                                           

    142-6.(2x+5)=10^2

    142-6.(2x+5)=100

           6.(2x+5)=142-100

           6.(2x+5)=42

               2x+5=42:6

               2x+5=7

                  2x=7-5

                  2x=2

                    x=1

Vậy x=1

a) 6

b) 81