Đáp án:

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`10`.

a) `5.125.625=5.5^3. 5^4=5^8`

b) `10.100.1000=10.10^2. 10^3=10^6`

c) `8^4. 16^5. 32=(2^3)^4.(2^4)^5. 2^5=2^12. 2^20. 2^5=2^37`

d) `27^4. 81^10=(3^3)^4.(3^4)^10=3^12. 3^40=3^52`

`11`.

e) `7. 2^13=7/8*8.2^13=7/8*2^3. 2^13=7/8*2^16`

`=>7/8<1=>7/8*2^16<2^16=>7. 2^13<2^16`

Vậy `7.2^13<2^16`.

f) `27^5. 49^8`

`=(3^3)^5.(7^2)^8`

`=3^15. 7^16`

`=3^15. 7^15. 7`

`=21^15 .7`

`=>21^15. 7>21^15`

`=>21^15<27^5. 49^8`

Vậy `21^15<27^5. 49^8`.

Hướng dẫn trả lời:

Bài 10:

a) `5.125.625.`

`= 5.5^{3}.5^{4}.`

`= 5^{1+3+4}.`

`= 5^{8}.`

b) `10.100.1000.`

`= 10.10^{2}.10^{3}.`

`= 10^{1 + 2 + 3}.`

`= 10^6.`

c) `8^{4}.16^{5}.32.`

`= (2^{3})^{4}.(2^{4})^{5}.2^{5}.`

`= 2^{12}.2^{20}.2^{5}.`

`= 2^{12 + 20 + 5}.`

`= 2^{37}.`

d) `27^{4}.81^{10}.`

`= (3^{3})^{4}.(3^{4})^{10}.`

`= 3^{12}.3^{40}.`

`= 3^{12 + 40}.`

`= 3^{52}.`

Bài 11:

e) Ta có: `7.2^{13}.`

`= 7/2^{3}.2^{3}.2^{13}.`

`= 7/8 .2^{16}.`

Vì `7/8 < 1` nên `7/8 .2^{16} < 2^{16}`.

Hay `7.2^{13} < 2^{16}.`

Vậy `7.2^{13} < 2^{16}.`

f) Ta có: `27^{5}.49^{8}.`

`= (3^{3})^{5}.(7^{2})^{8}.`

`= 3^{15}.7^{16}.`

`= 3^{15}.7^{15}.7.`

`= (3.7)^{15}.7.`

`= 21^{15}.7.`

Vì `1 < 7` nên `21^{15} < 21^{15}.7.`

Hay `21^{15} < 27^{5}.49^{8}.`

Vậy `21^{15} < 27^{5}.49^{8}.`

Đáp án:

Bài 10:

a) `= 5^{8}.`

b) `= 10^{6}.`

c) `= 2^{37}.`

d) `= 3^{52}.`

Bài 11:

e) `7.2^{13} < 2^{16}.`

f) `21^{15} < 27^{5}.49^{8}.`