`@` `\text {Ans}`
`\downarrow`
`k)`
\(27^4\div3^5\div81\)
`=`\(3^{12}\div3^5\div3^4\)
`=`\(3^{12-5-4}\)
`= 3^3`
`i)`
\(32^3\div8^5\div64\)
`=`\(2^{15}\div2^{15}\div2^6\)
`=`\(\dfrac{1}{2^6}=\dfrac{1}{64}\)
`l)`
\(125^5\div25^2\div625\)
`=`\(5^{15}\div5^4\div5^4\)
`=`\(5^7\)
`m)`
\(a^{30}\div\left(a^3\right)^9\)
`=`\(a^{30}\div a^{27}=a^3\)
\(27^4:3^5:81\\ =\left(3^3\right)^4:3^5:3^4\\ =3^{12}:3^5:3^4\\ =3^{12-5-4}\\ =3^3\\ 125^5:25^2:625\\ =\left(5^3\right)^5:\left(5^2\right)^2:5^4\\ =5^{15}:5^4:5^4\\ =5^{15-4-4}\\ =5^7\)
\(32^3:8^5:64\\ =\left(2^5\right)^3:\left(2^3\right)^5:2^6\\ =2^{15}:2^{15}:2^6\\ =2^{15-15-6}\\ =2^{-6}\)
\(a^{30}:\left(a^3\right)^9\\ =a^{30}:a^{27}\\ =a^{30-27}\\ =a^3\)
k: =3^12:3^5:3^4=3^3
e: =5^15:5^4:5^4=5^7
l: =2^15:2^15:2^6=1/64
m: =a^30:a^27=a^3
Áp dụng các công thức lũy thừa:
`@` \(a^m\div a^n=a^{m-n}\) (chia lũy thừa)
`@` \(\left(a^m\right)^n=a^{m\cdot n}\) (phép nâng lên lũy thừa)
Ex:
\(27^4=\left(3^3\right)^4=3^{3\cdot4}=3^{12}\)
\(32^3=\left(2^5\right)^3=2^{5\cdot3}=2^{15}\)
\(125^5=\left(5^3\right)^5=5^{3\cdot5}=5^{15}\)
`@` `\text {Kaizuu lv uuu}`