Question

calcule : a ) 2^5•2^-6

Answer 1

Boa Noite!

a) 2⁵ · 2⁻⁶ = 2⁵⁺⁽⁻⁶⁾ = 2⁵⁻⁶ = 2⁻¹ = $\frac{1}{2}$

b) 3⁵ · (3²)⁻² = 3⁵ · 3⁻⁴ = 3⁵⁺⁽⁻⁴⁾ = 3⁵⁻⁴ = 3¹ = 3

 $c) \frac{ 4^{-4} }{ 4^{-6} } = \frac{ \frac{1}{ 4^{4} } }{ \frac{1}{ 4^{6} } } = \frac{1}{ 4^{4} } . \frac{ 4^{6} }{1}}= \frac{ 4^{6} }{ 4^{4} }= 4^{6-4}= 4^{2} =16$

$d) \frac{ (5^{5})^{5}. (5^{3}) ^{5} }{ (5^{6})^{6} (5^{-2})^{2}}}= \frac{ (5^{5}) ^{5}. (5^{5}) ^{3}}{ ((5^{2}) ^{3})^{6} . (5^{2})^{-2}} = \frac{ (5^{5})^{5+3}}{ (5^{2})^{18-2}}= \frac{(5^{5})^{8}}{(5^{2})^{16}} = \frac{5^{40} }{ 5^{32} }= 5^{40-32}= 5^{8} =\\ \\ = 390625$
 
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