Question

a) Biểu diễn các lũy thừa sau thành những lũy thừa của cùng một cơ số:
\(\left(3^2\right)^3;\left(3^3\right)^2;\left(3^2\right)^5;9^8;27^6;81^{10}\)  ( Viết hai cách)
b) So sánh : \(5^{28}\)và \(26^{14}\)

hlepp meeeeee:<

Answer 1

a) Cách 1: \(\left(3^2\right)^3=3^{2.3}=3^6\)

\(\left(3^3\right)^2=3^{3.2}=3^6\)

\(\left(3^2\right)^5=3^{2.5}=3^{10}\)

\(9^8=\left(3^2\right)^8=3^{2.8}=3^{16}\)

\(27^6=\left(3^3\right)^6=3^{3.6}=3^{18}\)

\(81^{10}=\left(3^4\right)^{10}=3^{4.10}=3^{40}\)

Cách 2: \(\left(3^2\right)^3=9^3\)

\(\left(3^3\right)^2=3^{3.2}=\left(3^2\right)^3=9^3\)

\(\left(3^2\right)^5=9^5\)

\(9^8\)

\(27^6=\left(3^3\right)^6=3^{3.6}=3^{18}=3^{2.9}=\left(3^2\right)^9=9^9\)

\(81^{10}=\left(9^2\right)^{10}=9^{2.10}=9^{20}\)

Answer 2

Trả lời : 

b)

Ta có : \(5^{28}=5^{2.14}=\left(5^2\right)^{14}=25^{14}< 26^{14}\)

\(\Rightarrow5^{28}< 26^{14}\)

Answer 3

a) C1  : (3²)³ = 3^2.3 = 3⁶ ; 

C2 : (3²)³ = 3².3².3² = 3^{2 + 2 + 2} = 3⁶

b) C1 : (3³)² = 3^3.2 = 3⁶

C2 : (3³)² = 3³.3³ = 3^{3 + 3} = 3⁶

c) C1 (3²)⁵ = 3^2.5  = 3¹⁰

C2 (3²)⁵ = 3².3².3².3².3² = 3^{2 + 2 + 2 + 2 + 2} = 3¹⁰

d) 9⁸ = (3²)⁸ = 3^2.8 = 3¹⁶

9⁸ = (3.3)⁸ = 3⁸.3⁸ = 3¹⁶ 

e) 27⁶ = (3.3.3)⁶ = 3⁶.3⁶.3⁶ = 3^{6 + 6 +6} = 3¹⁸

27⁶ = (3³)⁶ = 3^3.6 = 3¹⁸

g) 81¹⁰ = (3.3.3.3)¹⁰ = 3¹⁰.3¹⁰.3¹⁰.3¹⁰ = 3^{10 + 10 + 10 + 10} = 3⁴⁰ ; 

81¹⁰ = (3⁴)¹⁰ = 3^4.10 = 3⁴⁰