Câu 4:

`a)(1/5)^5 .5^5`

`=(1/5 .5)^5`

`=1^5`

`=1`

`b)(0,125)³ .512`

`=(0,125)³.8³`

`=(0,125.8)³`

`=1³`

`=1`

`c)(0,25)^4 .1024`

`=(0,25)^4 . 4^5`

`=(0,25)^4 . 4^4 .4`

`=(0,25.4)^4 .4`

`=1^4 .4`

`=1.4`

`=4`

`d)(120³)/(40³)=(120/40)^3=3³=27`

`e)(390^4)/(130^4)=(390/130)^4=3^4=81`

`f)(3²)/((0,375)²)=(3/(0,375))^2=8²=64`

Câu 5:

`a)25³:5²=(5²)^3:5^2=5^6:5²=5^(6-2)=5^4`

`b)27³:3²=(3³)^3:3²=3^9:3²=3^(9-2)=3^7`

`c)(3/5)^15:(9/25)^5`

`=(3/5)^15:[(3/5)^2]^5`

`=(3/5)^15:(3/5)^10`

`=(3/5)^(15-10)`

`=(3/5)^5`

`d)25.5³. 1/625 .5²`

`=5².5³. 1/(5^4) .5²`

`=(5².5³.5²)/(5^4)`

`=(5^7)/(5^4)`

`=5³`

`e)4.32:(2³. 1/16)`

`=2².2^5:(2³. 1/(2^4))`

`=2².2^5:1/2`

`=2².2^5 .2`

`=2^(2+5+1)`

`=2^8`

Câu 6:

`a)5-(-5/11)^0+(1/3)^2:3`

`=5-1+(1/3)^2 . 1/3`

`=5-1+(1/3)^3`

`=4+1/27`

`=108/27+1/27`

`=109/27`

`b)5².3^5 .(3/5)²=5².3^5 .(3²)/(5²)=(5².3^5 .3²)/(5²)=3^7`

`c)(1/7)^2 . 1/7 .49²=(1/7 .49)^2 . 1/7=7². 1/7=7`

`d)(2^11 .9^2)/(3^5 .16^2)=(2^11 .(3^2)^2)/(3^5 .(2^4)^2)=(2^11 .3^4)/(3^5 .2^8)=(2^3)/3=8/3`

`e)(27^2 .8^5)/(6^6 .32^3)=((3^3)^2 .(2^3)^5)/((2.3)^6 .(2^5)^3)=(3^6 .2^15)/(2^6 .3^6 .2^15)=1/(2^6)=1/64`

Câu 7:

`a)(20^4)/(5^3)=((4.5)^4)/(5^3)=(4^4 .5^4)/(5^3)=4^4 .5=256.5=1280`

`b)(4^2 .4^3)/(2^10)=((2^2)^2 .(2^2)^3)/(2^10)=(2^4 .2^6)/(2^10)=1`
`c)(2^7 .9^3)/(6^5 .8^2)=(2^7 .(3^2)^3)/((2.3)^5 .(2^3)^2)=(2^7 .3^6)/(2^5 .3^5 .2^6)=(2^7 .3^6)/(2^11 .3^5)=3/(2^4)=3/16`
`d)(2^11 .9^2)/(3^5 .16^2)=(2^11 .(3^2)^2)/(3^5 .(2^4)^2)=(2^11 .3^4)/(3^5 .2^8)=(2^3)/3=8/3`

`e)121/((-11)^3)=(11^2)/(-11)^3=-1/11`

`f)(-2)^6/32=(-2)^6/(2^5)=-2`

Câu 8:

`a)x:((-1)/3)^3=-1/3`

`→x=(-1/3) . ((-1)/3)^3`

`→x=(-1/3)^4`

`b)(4/5)^5 .x=(4/5)^7`

`→x=(4/5)^7:(4/5)^5`

`→x=(4/5)^2`

`c)2.16≥2^x>4`

`→2.2^4≥2^x>2²`

`→2^5≥2^x>2²`

`→5≥x>2`

`→x∈{5;4;3}`

`d)9.27≤3^x≤243`

`→3².3³≤3^x≤3^5`

`→3^5≤3^x≤3^5`

`→5≤x≤5`

`→x=5`