Question

Can someone help me with this please I'm struggling

Answer 1

Solve :

$\sf \: \dfrac{ \: 45 \: {m}^{ - 6} \: {p}^{2} \: {v}^{12} \: }{ \: 15 \: {m}^{ - 2} \: {p}^{8} \: {v }^{ - 4} \: }$

Identity used :

$\sf \bullet \: \dfrac{ {a}^{p} }{ {a}^{q} } \: = \: {a}^{(p - q)}$

$\sf \bullet \: \: {a}^{ (- p)} \: = \dfrac{1}{ {a}^{p} }$

Solution :

$\sf \implies \dfrac{ \: 45 \: {m}^{ - 6} \: {p}^{2} \: {v}^{12} \: }{ \: 15 \: {m}^{ - 2} \: {p}^{8} \: {v }^{ - 4} \: }$

$\sf \implies \dfrac{ \: 45 }{15} \: \: \times \dfrac{{m}^{ - 6}}{ {m}^{ - 2} } \times \: \dfrac{{p}^{2}}{ {p}^{8} \:} \times \dfrac{{v}^{12}}{ {v }^{ - 4} } \:$

$\sf \implies \dfrac{ \:3 }{1} \: \: \times {m}^{( \: - 6 \: - \: ( - 2) \: )} \: \: \: \times \: \: {p}^{(2 - 8)} \: \: \times \: \: {v}^{( \: 12 - ( - 4) \: )\: }$

$\sf \implies \:3 \: \: \times {m}^{( \: - 6 \: + \: 2 \: ) \:} \: \: \: \times \: \: {p}^{( - 6)} \: \: \times \: \: {v}^{( \: 12 + \: 4 \: )\: }$

$\sf \implies \:3 \: \: \times {m}^{( \: - 4\: ) \:} \: \: \: \times \: \: {p}^{( - 6)} \: \: \times \: \: {v}^{( \: 16 \: )\: }$

$\sf \implies \:3 \: \: \times \dfrac{1}{{m}^{( \: 4\: ) \:}} \: \: \: \times \: \: \dfrac{1}{{p}^{( 6)} } \: \: \times \: \: {v}^{( \: 16 \: )\: }$

$\sf \implies \bold{ \: \dfrac{3 \: \times {v}^{ 16 } }{{m}^{ 4} \: {p}^{6} } }$

ANSWER :

Option 2