Question

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Answer 1

Step-by-step explanation:

$\frac{6( {8)}^{n + 1} + 16(2)^{3n - 2} }{10(2) ^{3n + 1} - 7(8)^{n} } \\ = \frac{6( {2}^{3} )^{n + 1} +16(2) ^{3n - 2} }{10 {(2)}^{3n + 1} - 7( {2}^{3}) ^{n} } \\ = \frac{6 {(2}^{3n + 3}) + 16( {2}^{3n - 2}) }{10( {2}^{3n + 1}) - 7(2 ^{3n} )} \\ = \frac{6( {2}^{3n} \times {2}^{3}) + 16 \frac{ {2}^{3n} }{ {2}^{2} } }{10( {2}^{3n} \times {2}^{1} ) - 7( {2}^{3n} ) } \\ = \frac{ {2}^{3n} ((6 \times {2}^{3} )+ ( \frac{16}{ {2}^{2} })) }{ {2}^{3n}((10 \times 2 )- (7)) } \\ = \frac{(6 \times {2}^{3} ) + (\frac{ {2}^{4} }{ {2}^{2} } )}{20 - 7} \\ = \frac{(6 \times 8) + ( {2}^{4 - 2}) }{13} \\ = \frac{48 + {2}^{2} }{ 13} \\ = \frac{48 + 4}{13} \\ = \frac{52}{13} = 4$

Answer 2

Answer:

6(8)n+1+16(2)3n−2

=10(2)3n+1−7(23)n6(23)n+1+16(2)3n−2=

10(23n+1)−7(23n)6(23n+3)+16(23n−2)

=10(23n×21)−7(23n)6(23n×23)+162223n

=23n((10×2)−(7))23n((6×23)+(2216))

=20−7(6×23)+(2224)

=13(6×8)+(24−2)

=1348+22

=1348+4

=1352=4