Dạng 4: So sánh hai biểu thức chứa lũy thừa

a, >

b, >

c, =

d, <

a, >

b, <

c, >

d, >

a, ${13}^2$ = 169 < 216 = ${13}^2$

b, $6^2+8^2$ = 100 < 196 = ${\left(6+8\right)}^2$

c, ${13}^2-9^2$ = 88 > 16 = ${\left(13-9\right)}^2$

d, $a^2+b^2$ < $a^2+b^2+2ab$ = ${\left(a+b\right)}^2\left(a;b\in N*\right)$

a) Cách 1: $2^{100}$ = ${\left(2^{10}\right)}^{10}={1024}^{10}$ > ${1024}^9$

Cách 2: ${1024}^9$ = ${\left(2^{10}\right)}^9$ = $2^{90}$ < $2^{100}$

b) $6.5^{29}$ > $5.5^{29}$ = $5^{30}$

c) $2^{98}$ = ${\left(2^2\right)}^{49}$ = $4^{49}$ < $9^{49}$

d) ${10}^{30}$ = ${\left({10}^3\right)}^{10}={1000}^{10}$; $2^{100}$ = ${\left(2^{10}\right)}^{10}$ = ${1024}^{10}$ nên ${10}^{30}$ < $2^{100}$