a) 27² : 25³

= (3³)² : (5²)³

= 3⁶ : 5⁶

 \(=\left(\frac{3}{5}\right)^6\)

b) 25⁴ : 2⁸

= (5²)⁴ : 2⁸

= 5⁸ : 2⁸

\(=\left(\frac{5}{2}\right)^8\)

mn vào lazi nhé

https://lazi.vn/users/dang_ky?u=dong.do-thi-thu

\(a,a^{\dfrac{3}{5}}\cdot a^{\dfrac{1}{2}}:a^{-\dfrac{2}{5}}=a^{\dfrac{3}{5}+\dfrac{1}{2}-\left(-\dfrac{2}{5}\right)}=a^{\dfrac{3}{2}}\\ b,\sqrt{a^{\dfrac{1}{2}}\sqrt{a^{\dfrac{1}{2}}\sqrt{a}}}\\ =\sqrt{a^{\dfrac{1}{2}}\sqrt{a^{\dfrac{1}{2}}\cdot a^{\dfrac{1}{2}}}}\\ =\sqrt{a^{\dfrac{1}{2}}\sqrt{a}}\\ =\sqrt{a^{\dfrac{1}{2}}\cdot a^{\dfrac{1}{2}}}\\ =\sqrt{a}\)

a: \(=3\cdot3^{\dfrac{1}{2}}\cdot3^{\dfrac{1}{.4}}\cdot3^{\dfrac{1}{8}}=3^{1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}}=3^{\dfrac{15}{16}}\)

b: \(=\sqrt{a\cdot\sqrt{a\cdot a^{\dfrac{1}{2}}}}\)

\(=\sqrt{a\cdot\sqrt{a^{\dfrac{3}{2}}}}=\sqrt{a\cdot a^{\dfrac{3}{4}}}=\sqrt{a^{\dfrac{7}{4}}}=a^{\dfrac{7}{4}\cdot\dfrac{1.}{2}}=a^{\dfrac{7}{8}}\)

c: \(=\dfrac{a^{\dfrac{1}{2}}\cdot a^{\dfrac{1}{3}}\cdot a^{\dfrac{1}{4}}}{\left(a^{\dfrac{1}{5}}\right)^3\cdot a^{\dfrac{2}{5}}}=\dfrac{a^{\dfrac{13}{12}}}{a}=a^{\dfrac{1}{12}}\)

\(a,\sqrt{2^3}=2^{\dfrac{3}{2}}\\ b,\sqrt[5]{\dfrac{1}{27}}=\sqrt[5]{3^{-3}}=3^{-\dfrac{3}{5}}\\ c,\left(\sqrt[5]{a}\right)^4=\sqrt[5]{a^4}=a^{\dfrac{4}{5}}\)

a) 10⁸.2⁸ = (10.2)⁸ = 20⁸

b) 10⁸ : 2⁸ = (10 : 2)⁸ = 5⁸

a, 10⁸  . 2⁸ = ( 10.2 )⁸ = 20⁸

b,10⁸ : 2⁸ = ( 10:2 )⁸ = 5⁸

a . 10 mũ 8 . 2 mũ 8 = 10 . 2 mũ 8 = 20 mũ 8

b . 10 mũ 8 :2 mũ 8 =10 :2 mũ 8 =5 mũ 8

1a) 7^4    b) 15^4    c) 1000^2      d)a^3.b^3

e)m^4+p^2       f)a^7-a^2.b^2       

2)a)2^6    b) 5^8    c) 3^10  d)3^14

e) a^6   f)b^5

Bài 6: 

a: \(2^{27}=8^9\)

\(3^{18}=9^9\)

b: Vì \(8^9< 9^9\)

nên \(2^{27}< 3^{18}\)