Question

Comparati:
a) $8^{7}$ si $2^{20}$
b) $9^{5}$ si $4^{10}$
c) $2^{4}$ si $4^{2}$
d) $2^{21}$ si $3^{14}$

Answer 1

Răspuns:

Explicație pas cu pas:

a)

8⁷=(2³)⁷=2²¹

2²⁰=2²⁰

2²¹>2²⁰

8⁷>2²⁰

-

b)

9⁵=(3²)⁵=3¹⁰

4¹⁰=4¹⁰

3¹⁰<4¹⁰

9⁵< 4¹⁰

-

c)

2⁴=2⁴

4²=(2²)²= 2⁴

2⁴=2⁴

2⁴=4²

-

d)

2²¹=(2³)⁷=8⁷

3¹⁴=(3²)⁷=9⁷

8⁷<9⁷

2²¹<3¹⁴

Answer 2

Explicație pas cu pas:

a)

$8^{7} = {( {2}^{3} )}^{7} = {2}^{21}$

${2}^{21} > 2^{20} \implies {8}^{7} > 2^{20}$

b)

$9^{5} = ( {3}^{2} )^{5} = {3}^{10}$

${3}^{10} < 4^{10} \implies 9^{5} < 4^{10}$

c)

$4^{2} = ({2}^{2})^{2} = {2}^{4}$

${2}^{4} = {2}^{4} \implies 2^{4} = 4^{2}$

d)

$2^{21} = 2^{3 \cdot 7} = {( {2}^{3} )}^{7} = {8}^{7}$

$3^{14} = 3^{2 \cdot 7} = {( {3}^{2} )}^{7} = {9}^{7}$

${8}^{7} < {9}^{7} \implies 2^{21} < 3^{14}$