Question

[Khánh Vinh]

So sánh các số sau:  Help me!

a)\(27^{11}\)và \(81^8\)

^{b) \(2^{225}\)và \(3^{150}\)}

^{c) \(2^{500}\)}và \(5^{200}\)

d) \(625^5\)và. \(125^7\)

e) \(5^{100}\)và \(8^{75}\)

f) \(7.2^{13}\)và \(2^{16}\)

g) \(27^{50}\)và \(240^{30}\)

h) \(63^9\)và \(17^{14}\)

Answer 1

[Nguyễn Việt Hoàng]

a) Ta có :

\(\hept{\begin{cases}27^{11}=\left(3^3\right)^{11}=3^{33}\\81^8=\left(3^4\right)^8=3^{32}\end{cases}}\)

Vì 3³³ > 3³²

=> 27¹¹ > 81⁸

b) Ta có:

\(\hept{\begin{cases}2^{225}=\left(2^3\right)^{75}=8^{75}\\3^{150}=\left(3^2\right)^{75}=9^{75}\end{cases}}\)

Vì 8⁷⁵ < 9⁷⁵

=> 2²²⁵ < 3¹⁵⁰

Thôi còn lại bn tự làm nốt nha . Nhìn mà nản !!

Answer 2

[l҉o҉n҉g҉ d҉z҉]

a) \(\hept{\begin{cases}27^{11}=\left(3^3\right)^{11}=3^{33}\\81^8=\left(3^4\right)^8=3^{32}\end{cases}}\)

3³³ > 3³² => 27¹¹ > 81⁸

b) \(\hept{\begin{cases}2^{225}=\left(2^3\right)^{75}=8^{75}\\3^{150}=\left(3^2\right)^{75}=9^{75}\end{cases}}\)

8⁷⁵ < 9⁷⁵ => 2²²⁵ < 3¹⁵⁰

c) \(\hept{\begin{cases}2^{500}=\left(2^5\right)^{100}=32^{100}\\5^{200}=\left(5^2\right)^{100}=25^{100}\end{cases}}\)

32¹⁰⁰ > 25¹⁰⁰ => 2⁵⁰⁰ > 5²⁰⁰

d) \(\hept{\begin{cases}625^5=\left(5^4\right)^5=5^{20}\\125^7=\left(5^3\right)^7=5^{21}\end{cases}}\)

5²⁰ < 5²¹ => 625⁵ < 125⁷

e) \(\hept{\begin{cases}5^{100}=\left(5^4\right)^{25}=625^{25}\\8^{75}=\left(8^3\right)^{25}=512^{25}\end{cases}}\)

625²⁵ > 512²⁵ => 5¹⁰⁰ > 8⁷⁵

f) \(2^{16}=2^3\cdot2^{13}=8\cdot2^{13}\)

7 < 8 => 7.2¹³ < 8.2¹³ => 7.2¹³ < 2¹⁶

g) Ta có \(\frac{27^{50}}{240^{30}}=\frac{\left(3^3\right)^{50}}{3^{30}\cdot80^{30}}=\frac{3^{150}}{3^{30}\cdot80^{30}}=\frac{3^{120}}{80^{30}}=\frac{\left(3^4\right)^{30}}{80^{30}}=\frac{81^{30}}{80^{30}}\)

Vì 81³⁰ > 80³⁰ => 81³⁰/80³⁰ > 1 => 27⁵⁰/240³⁰ > 1 => 27⁵⁰ > 240³⁰

h) Ta có \(\hept{\begin{cases}63^9< 64^9=\left(2^6\right)^9=2^{54}\left(1\right)\\16^{14}=\left(2^4\right)^{14}=2^{56}< 17^{14}\left(2\right)\end{cases}}\)

Từ (1) và (2) => 63⁹ < 2⁵⁴ < 2⁵⁶ < 17¹⁴

=> 63⁹ < 17¹⁴