Giải Toán 7 bài 6: Lũy thừa của một số hữu tỉ (tiếp theo)

Các câu sai là a, c, d, f

Các câu đúng là b, e

Sửa lại:

a) \((-5)^2 .(-5)^3 = (-5)^5\)

c) \((0,2)^{10} : (0,2)^5 = (0,2)^5\)

d) \(\left[\left(- \dfrac{1}{7}\right)^2\right]^4 = \left(- \dfrac{1}{7}\right)^8;\)

f) \(\dfrac{8^{10}}{4^8} = \dfrac{(2.4)^{10}}{4^8} = \dfrac{2^{10}.4^{10}}{4^8} = 2^{10}.4^2 = 2^{10}.2^4 = 2^{14}\)

a)\(\left(\dfrac{1}{2}\right)^m = \dfrac{1}{32}\)

\(\Leftrightarrow \left(\dfrac{1}{2}\right)^m = \left(\dfrac{1}{2}\right)^5\)

\(\Rightarrow m = 5\)

b) \(\dfrac{343}{125} = \left(\dfrac{7}{5}\right)^n\)

\(\Leftrightarrow \left(\dfrac{7}{5}\right)^3 = \left(\dfrac{7}{5}\right)^n\)

\(\Rightarrow n = 3\)

a) 10⁸ . 2⁸ = (10.2)⁸ = 20⁸

b) 10⁸ : 2⁸ = (10:2)⁸ = 5⁸

c) 25⁴ . 2⁸ = 5⁸ . 2⁸ = 10⁸

d) 15⁸ . 9⁴ = 15⁸ . 3⁸ = 45⁸

e) 27² : 25³ = (3³)² : (5²)³ = 3^3.2 : 5^2.3 = 3⁶ : 5⁶

^{\(= \left(\dfrac{3}{5}\right)^6\)}

a) \(\dfrac{4^2.4^3}{2^{10}} = \dfrac{4^5}{2^{10}} =\dfrac{(2^2)^5}{2^{10}} = \dfrac{2^{10}}{2^{10}} =1\)

b) \(\dfrac{(0,6)^5}{(0,2)^6} = \dfrac{(3.0,2)^5}{(0,2).(0,2)^5} = \dfrac{3^{5}.(0,2)^5}{(0,2).(0,2)^5} = \dfrac{3^{5}}{(0,2)} = \dfrac{243}{(0,2)} = 1215\)

c) \(\dfrac{2^7.9^3}{6^5.8^2} = \dfrac{2^2.2^5.(3^2)^3}{(2.3)^5.(2^3)^2} = \dfrac{2^2.2^5.3^6}{2^5.3^5.2^6} = \dfrac{3}{2^4} = \dfrac{3}{16}\)

d) \(\dfrac{6^3 + 3.6^2 + 3^3}{-13}\)

\(= \dfrac{(2.3)^3 + 3.(2.3)^2 + 3^3}{-13}\)

\(= \dfrac{2^3.3^3 + 2^2.3^3 + 3^3}{-13}\)

\(= \dfrac{3^3(2^3 + 2^2 + 1)}{-13}\)

\(= \dfrac{27.13}{-13} = -27\)

a) Ta có 2²⁷ = (2³)⁹ = 8⁹

3¹⁸ = (3²)⁹ = 9⁹

b) Vì 8 < 9 nên 8⁹ < 9⁹ hay 2²⁷ < 3¹⁸

a) x¹⁰ = x³ . x⁷

b) x¹⁰ = (x²)⁵

c) x¹⁰ = x¹² : x²

a)\(\left(\dfrac{3}{7} + \dfrac{1}{2} \right)^2 = \left(\dfrac{6 + 7}{14} \right)^2 = \left(\dfrac{13}{14} \right)^2 = \dfrac{169}{196}\)

b) \(\left(\dfrac{3}{4} - \dfrac{5}{6} \right)^2 = \left(\dfrac{9 - 10}{12} \right)^2 = \left(\dfrac{-1}{12} \right)^2 = \dfrac{1}{144}\)

c) \(\dfrac{5^4.20^4}{25^5.4^5} = \dfrac{5^4.(5.4)^4}{(5.5)^5.4^5} =\dfrac{5^4.5^4.4^4}{5^5.5^5.4^5} = \dfrac{1}{5.5.4} = \dfrac{1}{100}\)

d)\(\left(\dfrac{-10}{3} \right)^5 . \left(\dfrac{-6}{5} \right)^4 = \dfrac{(-2.5)^5}{3^5}.\dfrac{(2.3)^4}{5^4} = \dfrac{-2^5.5^5.2^4.3^4}{3^5.5^4} = \dfrac{-2^9.5}{3} = \dfrac{-2560}{3}\)

a)\(\left(1 + \dfrac{2}{3} - \dfrac{1}{4}\right). \left( \dfrac{4}{5} - \dfrac{3}{4}\right)^2\)

\(= \left(\dfrac{12 + 8 - 3}{12}\right). \left(\dfrac{16 - 15}{20}\right)^2\)

\(= \dfrac{17}{12}. \left(\dfrac{1}{20}\right)^2\)

\(= \dfrac{17}{4800}\)

b) \(2 : \left(\dfrac{1}{2} - \dfrac{2}{3}\right)^3\)

\(=​​ 2 : \left(\dfrac{3 - 4}{6}\right)^3\)

\(= 2 : \left(-\dfrac{1}{6}\right)^3\)

\(= 2 : \dfrac{-1}{216}\)

\(= 2 . \dfrac{-216}{1} = -432\)

a) \(\dfrac{16}{2^n} = 2 \Leftrightarrow 2^n.2 = 16 \Leftrightarrow 2^{n + 1} = 2^4 \Leftrightarrow n + 1 = 4 \Leftrightarrow n = 3\)

b)\(\dfrac{(-3)^n}{81} = -27 \Leftrightarrow (-3)^n = (-3)^3.3^4 \Leftrightarrow (-3)^n = (-3)^7 \Leftrightarrow n = 7\)

c) \(8^n : 2^n = 4 \Leftrightarrow \left(\dfrac{8}{2}\right)^n = 2^2 \Leftrightarrow 4^n = 2^2 \Leftrightarrow 2^{2n} = 2^2 \Leftrightarrow 2n = 2 \Leftrightarrow n = 1\)

S = 2² + 4² + 6² + ... + 20²

= (2.1)² + (2.2)² + (2.3)² ... (2.10)²

= 2².1² + 2².2² + 2².3² + ... + 2².10²

= 2² (1² + 2² + ... + 10² )

= 4 . 385 = 1540