Question

1.so sánh:

a)\(5^6\)và\(\left(-2\right)^{14}\)

b)\(9^5\)và \(27^3\)

c) \(\left(\frac{1}{8}\right)^6\) và \(\left(\frac{1}{32}\right)^4\)

Answer 1

b) Ta có: \(9^5=\left(3^2\right)^5=3^{10}\) 

             \(27^3=\left(3^3\right)^3=3^9\)

Vì 10 > 9 => 3¹⁰ > 3⁹

Vậy 9⁵ > 27³

Answer 2

1. So sánh : 

b) 9^5 và 27^3 

9^5 = ( 3^2 )^5 = 3^10

27^3 = ( 3^3 )^3  = 3^9 

Vì 3^10 > 3^9 => 9^5 > 27^3 

Vậy 9^5 > 27^3 

c) \(\left(\frac{1}{8}\right)^6\)và \(\left(\frac{1}{32}\right)^4\)

\(\left(\frac{1}{8}\right)^6=\left(\frac{1}{2}\right)^{3.6}=\left(\frac{1}{2}\right)^{18}\)

\(\left(\frac{1}{32}\right)^4=\left(\frac{1}{2}\right)^{5.4}=\left(\frac{1}{2}\right)^{20}\)

Vì ( 1/2)^18 < (1/2)^20 => (1/8)^6 < (1/32)^4 

Vậy (1/8)^6 < (1/32)^4

Answer 3

a)  ta có \(\hept{\begin{cases}\left(-2\right)^{14}=\left(-2^7\right)^2=128^2\\5^6=5^{3.2}=\left(5^3\right)^2=125^2\end{cases}}\)

vì \(128>125\Rightarrow128^2>125^2\Rightarrow5^6< \left(-2\right)^{14}\)

vậy \(5^6< \left(-2\right)^{14}\)

b) ta có \(\hept{\begin{cases}27^3=\left(3^3\right)^3=3^9\\9^5=\left(3^2\right)^5=3^{10}\end{cases}}\)

vì \(3^{10}>3^9\Rightarrow9^5>27^3\)

vậy \(9^5>27^3\)

c) ta có \(\hept{\begin{cases}\left(\frac{1}{8}\right)^6=\left(\frac{1}{2}\right)^{18}\\\left(\frac{1}{32}\right)^4=\left(\frac{1}{2}\right)^{20}\end{cases}}\)

vì \(18< 20\Rightarrow\left(\frac{1}{2}\right)^{18}< \left(\frac{1}{2}\right)^{20}\Rightarrow\left(\frac{1}{8}\right)^6< \left(\frac{1}{32}\right)^4\)

vậy \(\left(\frac{1}{8}\right)^6< \left(\frac{1}{32}\right)^4\)

Answer 4

Nguyễn bá lương: \(\left(-2^7\right)=-128\)