Question

please solve this question...

Answer 1

$\frac{ {64}^{ \frac{a}{6} } }{ {4}^{a} } \times \frac{ {2}^{2a + 1} }{ {2}^{a - 1} } \\ \\ = \frac{ {2}^{6 \times \frac{a}{6} } }{ {2}^{2 \times a} } \times \frac{ {2}^{2a + 1} }{ {2}^{a - 1} } \\ \\ = \frac{ {2}^{ a} }{ {2}^{2a} } \times \frac{ {2}^{2a + 1} }{ {2}^{a - 1} } \\ \\ \bf \: using \: the \: identity \\ \bf \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ = {2}^{a - 2a} \times {2}^{(2a + 1) - (a - 1)} \\ \\ = {2}^{ - a} \times {2}^{2a + 1 - a + 1} \\ \\ = {2}^{ - a} \times {2}^{a + 2} \\ \\ \bf \: using \: the \: identity \\ \bf \: {a}^{m} \times {a}^{n} = {a}^{ m+ n} \\ \\ = {2}^{ ( - a) + (a + 2)} \\ \\ = {2}^{ - a + a + 2} \\ \\ \bf \: = {2}^{2} \: \: or \: \: 4$

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Answer 2

$\underline{\bold{Solution:-}}$

$\frac{ {64}^{ \frac{a}{6} } }{ {4}^{a} } \times \frac{ {2}^{2a + 1} }{ {2}^{a - 1} } \\ \\ = \frac{ {( {2}^{6} )}^{ \frac{a}{6} } }{ {( {2}^{2}) }^{a} } \times \frac{ {2}^{2a + 1} }{ {2}^{a - 1} } \\ \\ = \frac{ {2}^{6 \times \frac{a}{6} } }{ {2}^{2 \times a} } \times \frac{ {2}^{2a + 1} }{ {2}^{a - 1} }$

$= \frac{ {2}^{ a } }{ {2}^{2a} } \times \frac{ {2}^{2a + 1} }{ {2}^{a - 1} }$

• If a number is divided by another number of same base , then there power gets subtracted.

And it's identity is

$\boxed{\frac{ { x}^{m} }{ {x}^{n} } = {x}^{m - n}}$

$= {2}^{a - 2a} \times {2}^{2a + 1 - a + 1} \\ \\ = {2}^{-a} \times {2}^{a + 2}$

• If two numbers of same base are multiplied ,then there powers are added.

And it's identity is

$\boxed{ {x}^{m} \times {x}^{n} = {x}^{m + n}}$

$= {2}^{-a + a + 2} \\ \\ = {2}^{2}$

$\boxed{\bold{= 4}}$

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