Question

Simplify

please explain with steps and correct answers will be marked as brainliest.​

Answer 1

$\longmapsto \rm{ \bf{1}}$

Step-by-step explanation:

★Given -

• $\rm{ \bf\dfrac{16 \times {2}^{n + 1} - 4 \times {2}^{n} }{ 16 \times {2}^{n + 2} - 2 \times {2}^{n + 2} } }$

★To do -

• Simplify.

★Solution -

$\longmapsto \rm{ \bf\dfrac{16 \times {2}^{n + 1} - 4 \times {2}^{n} }{ 16 \times {2}^{n + 2} - 2 \times {2}^{n + 2} } }$

$\longmapsto \rm{ \bf\dfrac{16 \times {2}^{n } \times 2 - 4 \times {2}^{n} }{ 16 \times {2}^{n + 2} - 2 \times {2}^{n + 2} } }$

$\longmapsto \rm{ \bf\dfrac{ {2}^{n} (16 \times 2 - 4 ) }{ {2}^{n + 2} (16 - 2 ) } }$

$\longmapsto \rm{ \bf\dfrac{ {2}^{n} (32 - 4 ) }{ {2}^{n } \times 2(16 - 2 ) } }$

$\longmapsto \rm{ \bf\dfrac{ {2}^{n} \times (28) }{ {2}^{n } \times 2(14 ) } }$

$\longmapsto \rm{ \bf\dfrac{ \cancel{{2}^{n} \times 28} \: \: ^{1} }{ \cancel{ {2}^{n } \times 28 } \: \: ^{1} } }$

$\longmapsto \rm{ \bf \orange{1}}$

★More to know -

• $\rm{ \bf{a^{m + n} = {a}^{m} {a}^{n} }}$