Question

1. So Sánh 2 lũy thừa sau:

\(a,4^{72}v\text{à}8^{48}\)

\(b,5^{127}v\text{à}2^{254}\)

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Answer 1

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\(a,4^{72}v\text{à}8^{48}\)

TA CÓ:\(4^{72}=\left(2^2\right)^{72}=2^{144}\)

\(8^{48}=\left(2^3\right)^{48}=2^{144}\)

\(\Rightarrow4^{72}=8^{48}\)

\(b,5^{127}v\text{à}2^{254}\)

TA CÓ:\(2^{252}2^{2\times127}=\left(2^2\right)^{127}=4^{127}\)

\(5^{127}>4^{127}\left(v\text{ì5>4}\right)\)\(5^{127}>4^{127}\left(v\text{ì}5>4\right)\)

\(\Rightarrow5^{127}>2^{254}\)

Answer 2

a) Ta có : 4⁷² = 4^3.24 = (4³)²⁴ = 64²⁴

                8⁴⁸ = 8^2.24 = (8²)²⁴ = 64²⁴

Ta thấy : 64²⁴ = 64²⁴ => 4⁷² = 8⁴⁸

b) Ta có : 2²⁵⁴ = 2^2.127 = (2²)¹²⁷ = 4¹²⁷

Vì 5 > 4 => 5¹²⁷ > 2²⁵⁴

Answer 3

\(a,4^{72}=\left(2^2\right)^{72}=2^{144}\)

    \(8^{48}=\left(2^3\right)^{48}=2^{144}\)

\(\Rightarrow4^{72}=8^{48}\)

\(b,2^{254}=\left(2^2\right)^{127}=4^{127}< 5^{127}\)

\(\Rightarrow2^{254}< 5^{127}\)