Question

So sanh cac luy thua sau:

2¹⁰⁰ va 10249    

9¹² va 27⁷

125⁸⁰ va 25⁴⁸

10 ³⁰ va 2¹⁰⁰               

Answer 1

1/ Ta có:\(1024^9=\left(2^{10}\right)^9=2^{90}\)

Vì 2¹⁰⁰>2⁹⁰ nên 2¹⁰⁰>1024⁹

2/ Ta có:

\(9^{12}=\left(3^2\right)^{12}=3^{24}\)

\(27^7=\left(3^3\right)^7=3^{21}\)

Vì 3²⁴>3²¹ nên 9¹²>27⁷

3/  Vì \(\hept{\begin{cases}125>25\\80>48\end{cases}\Rightarrow125^{80}>25^{48}}\)

4/ Ta có:

\(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

Vì 1000¹⁰<1024¹⁰ nên 10³⁰<2¹⁰⁰