Question

The value of: [(27)^2/3 × (8)^2/3]/9^3/2 is(a) 1/3(b) 2/3(c) 3/3(d) 4/3​

Answer 1

Step-by-step explanation:

➤ Given:-

$\sf{\frac{(27 {)}^{ \frac{2}{3} } \times (8 {)}^{ \frac{2}{3} } }{(9 {)}^{ \frac{3}{2} } } }$

➤ To find:-

• ${\sf Simplifyed \:form = ?}$

➤ Solution:-

$\textsf{We have,}$

$\sf{\frac{(27 {)}^{ \frac{2}{3} } \times (8 {)}^{ \frac{2}{3} } }{(9 {)}^{ \frac{3}{2} } } }$

$\sf \leadsto \: {\frac{( {3}^{3} {)}^{ \frac{2}{3} } \times ( { {2}^{3} )}^{ \frac{2}{3} } }{( {3}^{2} {)}^{ \frac{3}{2} } } }$

$\sf \leadsto \: \frac{ {3}^{ \cancel3 \times \frac{2}{ \cancel3} } \times {2}^{ \cancel3 \times \frac{2}{ \cancel3} } }{ {3}^{ \cancel2 \times \frac{3}{ \cancel2} } }$

$\sf \leadsto \: \frac{ {3}^{2} \times {2}^{2} }{(3 {)}^{3} }$

$\sf \leadsto \: \frac{ {2}^{2} }{ {3}^{(3 - 2)}}$

$\sf \leadsto \: \frac{ {2}^{2} } { {3}^{1} }$

$\sf \leadsto \: \frac{2 \times 2}{3}$

$\sf \leadsto \: \frac{4}{3}$