Question

Which expression is equivalent?

Answer 1

Answer:

y⁸/x¹⁰

Step-by-step explanation:

$\sf{\large{( \frac{ {x}^{ - 4}y }{ {x}^{ - 9} {y}^{5} } ) ^{2} }}$

$\large{ \sf{= \frac{ {x}^{ - 4 \times 2} {y}^{2} }{ {x}^{ - 9 \times 2} {y}^{5 \times 2} } }}$

$\large{ \sf{= \frac{ {x}^{ - 8} {y}^{2} }{ {x}^{ - 18} {y}^{10} } }}$

$\large{ \sf{ = {x}^{ - 8 - ( - 18)} {y}^{2 - 10} }}$

$\large{ \sf{ = {x}^{ - 8 + 18} {y}^{ - 8} }}$

$\large{ \sf{ = {x}^{10} {y}^{ - 8} }}$

$\large{ \sf{ = \frac{ {x}^{10} }{ {y}^{8} } }}$

$\large{ \sf{ = \frac{ {y}^{8} }{ {x}^{10} } }}$