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Răspuns:

Explicație pas cu pas:

a)

8⁷=(2³)⁷=2²¹

2²⁰=2²⁰

2²¹>2²⁰

8⁷>2²⁰

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b)

9⁵=(3²)⁵=3¹⁰

4¹⁰=4¹⁰

3¹⁰<4¹⁰

9⁵< 4¹⁰

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c)

2⁴=2⁴

4²=(2²)²= 2⁴

2⁴=2⁴

2⁴=4²

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d)

2²¹=(2³)⁷=8⁷

3¹⁴=(3²)⁷=9⁷

8⁷<9⁷

2²¹<3¹⁴

Explicație pas cu pas:

a)

[tex]8^{7} = {( {2}^{3} )}^{7} = {2}^{21} [/tex]

[tex]{2}^{21} > 2^{20} \implies {8}^{7} > 2^{20}[/tex]

b)

[tex]9^{5} = ( {3}^{2} )^{5} = {3}^{10}[/tex]

[tex]{3}^{10} < 4^{10} \implies 9^{5} < 4^{10}[/tex]

c)

[tex]4^{2} = ({2}^{2})^{2} = {2}^{4} [/tex]

[tex]{2}^{4} = {2}^{4} \implies 2^{4} = 4^{2}[/tex]

d)

[tex]2^{21} = 2^{3 \cdot 7} = {( {2}^{3} )}^{7} = {8}^{7} [/tex]

[tex]3^{14} = 3^{2 \cdot 7} = {( {3}^{2} )}^{7} = {9}^{7}[/tex]

[tex]{8}^{7} < {9}^{7} \implies 2^{21} < 3^{14}[/tex]