Question

comparati numerele, scriindule ca puteri cu același exponent a) a=2³⁶,b=3²⁴​

Answer 1

$a = {2}^{36} = {2}^{3 \times 12} = {( {2}^{3}) }^{12} = {8}^{12}$

$b = {3}^{24} = {3}^{2 \times 12} = {( {3}^{2}) }^{12} = {9}^{12}$

${8}^{12} < {9}^{12}$

$a < b$

Answer 2

Răspuns:

Explicație pas cu pas:

$\bf a = 2^{36}= \big(2^{6}\big)^{6} = \purple{ \boxed{\bf ~64^{6~}}}$

$\bf b = 3^{24}= \big(3^{4}\big)^{6} = \red{ \boxed{\bf ~81^{6~}}}$

$\bf \pink{ \underline{\bf ~81^{6}~>~ 64^{6}}}$

$\bf \pink{ \bf ~b~>~ a}$