Bài 5: Lũy thừa của một số hữu tỉ

a) 8¹⁴=(2³)¹⁴=2^3*14=2⁴²

16¹⁰=(8*2)¹⁰=8¹⁰*2¹⁰=(2³)¹⁰*2¹⁰=2³⁰*2¹⁰=2⁴⁰

Vì 2⁴² > 2⁴⁰ nên 8¹⁴ > 16¹⁰

b) 2³³=(2³)¹¹=8¹¹

3²²=(3²)¹¹=9¹¹

Vì 8¹¹ < 9¹¹ nên 2³³ < 3²²

c) 3⁶³ > 3⁶⁰=(3⁴)¹⁵=81¹⁵

Vì 81¹⁵ > 54² nên 3⁶³ > 54²

* Trả lời:

\(8^7-2^{18}⋮14\)

\(\Leftrightarrow\left(2^3\right)^7-2^{18}⋮14\)

\(\Leftrightarrow2^{21}-2^{18}⋮14\)

\(\Leftrightarrow2^{18}.\left(2^3-1\right)⋮14\)

\(\Leftrightarrow2^{18}.7⋮14\)

\(\Leftrightarrow2^{17}.2.7⋮14\)

\(\Leftrightarrow2^{17}.14⋮14\)

\(\Rightarrow8^7-2^{18}⋮14\)

8⁷-2¹⁸ =(2³)⁷-2¹⁸ =2²¹-2¹⁸=2¹⁸*(2³-1) =2¹⁸*7 =2¹⁷*2*7 =2¹⁷*14 chia hết cho 14

=> 8⁷-2¹⁸ chia hết cho 14 (đpcm)

Có \(\left(-2\dfrac{3}{4}+\dfrac{1}{2}\right)^2\)=\(\left(\dfrac{-5}{4}+\dfrac{2}{4}\right)^2\)=\(\left(\dfrac{-3}{4}\right)^2\)=\(\dfrac{\left(-3\right)^2}{4^2}=\dfrac{9}{16}\)

Có \(\dfrac{\left(0,125\right)^5.\left(2,4\right)^5}{\left(-0,3\right)^5.\left(0,01\right)^3}=\dfrac{\left(0,125.2,4\right)^5}{\left(-0,3\right)^5.\left(0,01\right)^3}=\dfrac{\left(0,3\right)^5}{\left(-0.3\right)^5.\left(0,01\right)^3}=\dfrac{1}{-1.\left(0,01\right)^3}=\dfrac{1}{-\left(0,01\right)^3}\)

https://iostudy.net/ref/133587

Có : \(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\dfrac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}=\dfrac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}=\dfrac{1-3}{1+5}=\dfrac{1}{3}\)

\(\left(x-3\right)^2=1\)

\(\Rightarrow x-3=1\) ( Quy ước \(1^x=1\))

\(=>x=1+3=4\)

Có \(\left(x-3\right)^2=1\)

=> \(\left(x-3\right)^2=1^2\) hoặc \(\left(x-3\right)^2=\left(-1\right)^2\)

=> x-3=1 hoặc x-3=-1

=> x=4 hoặc x=2

Vậy x=4 hoặc x=2

\(\left(\dfrac{2}{3}\right)^3\)=\(\dfrac{8}{27}\) b)\(\left(-2\dfrac{3}{4}\right)^2\)=\(\dfrac{14641}{256}\) c) (0,6)⁴=0.1296

\(\left(\dfrac{-1}{4}\right)^4\)=\(\dfrac{1}{256}\) d)\(\left(\dfrac{-1}{2}\right)^5\)=\(\dfrac{-1}{32}\)

Chúc bạn học tốt

Có 44³⁹=44^3.13=(44³)¹³=85184¹³

33⁵²= 33^4.13=(33⁴)¹³=1185921¹³

mà 85184¹³ < 1185921¹³

<=> 44³⁹<33⁵²

a) Có \(\dfrac{2^8.9^2}{6^4.8^2}\)=\(\dfrac{2^8.3^4}{3^4.2^42^6}\)=\(\dfrac{2^8.3^4}{3^4.2^{10}}\)=\(\dfrac{2^8}{2^{10}}\)=\(\dfrac{1}{4}\)

b) Có \(\left(2^{-1}+3^{-1}\right):\left(2^{-1}-3^{-1}\right)+\left(2^{-1}.2^0\right).2^3\)

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

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

= \(\dfrac{\dfrac{5}{6}}{\dfrac{1}{6}}+2^2\)=5+8=13

a) Có \(\left(\dfrac{-1}{8}\right)^{25}=\left(\dfrac{-1}{2^3}\right)^{25}=\dfrac{-1^{25}}{\left(2^3\right)^{25}}=\dfrac{-1}{2^{75}}\)

\(\left(\dfrac{-1}{128}\right)^{13}=\left(\dfrac{-1}{2^7}\right)^{13}=\dfrac{-1^{13}}{\left(2^7\right)^{13}}=\dfrac{-1}{2^{91}}\)

mà \(\dfrac{1}{2^{75}}>\dfrac{1}{2^{91}}\) <=>\(\dfrac{-1}{2^{75}}< \dfrac{-1}{2^{91}}\)

<=> \(\left(\dfrac{-1}{8}\right)^{25}\) < \(\left(\dfrac{-1}{128}\right)^{13}\)

b) Có 32³⁰ =( 2⁵)³⁰ = 2¹⁵⁰=(2⁶)²⁵=64²⁵

9⁷⁵ = (3³)⁷⁵= 3²²⁵=(3⁹)²⁵=19683²⁵

mà 64²⁵<19683²⁵ <=>32³⁰<9⁷⁵

a, đầu bài sai hay sao đó bn

b,\(\dfrac{2}{3}\).3^x+1 - 7.3^x = -405

3^x(\(\dfrac{2}{3}\).3 - 7) = -405

3^x . (-5) = -405

3^x = 81 mà 81 = 3⁴ suy ra x = 4