Question

1. Tính

\(\left(0,25\right)^4.1024\)

2. So sánh

\(2^{91}\) và \(5^{35}\)

3. Tìm giá trị biểu thức

a) \(\dfrac{45^{10}.5^{20}}{75^{15}}\) b) \(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}\) c) \(\dfrac{2^{15}.9^4}{6^6.8^3}\)

Answer 1

1.Tính

(0,25)⁴.1024=(1/4)⁴.1024=4

2.So sánh

2⁹¹=(2¹³)⁷=8192⁷

5³⁵=(5⁵)⁷=3125⁷

Mà 8192>3125=> 8192⁷>3125⁷

=> 2⁹¹>5³⁵

3. Tìm giá trị biểu thức

a) \(\dfrac{45^{10^{ }}.5^{20^{ }}}{75^{15}}=\dfrac{\left(3^{2^{ }}.5\right)^{10^{ }}.5^{20}}{^{ }\left(3.5^2\right)^{15}}=\dfrac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5=243\)

b)\(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}=\dfrac{\left(2.0,4\right)^5}{0,4.0,4^5}=\dfrac{2^{5^{ }}.0,4^5}{0,4.0,4^5}=\dfrac{2^5}{0,4}=80\)

c)\(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15^{ }}.3^8}{3^6.2^6.2^9}=\dfrac{2^{15}.3^8}{3^6.2^{15}}=3^2=9\)

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