√(3×5^(−3)÷3×√(3^(−1)×√(5)×6×√(3×5^(6) = 3/5. prove tha
Answers
Answer:
So from the above terms we have proved that LHS = RHS
{ √(3*5^-3) ÷ (∛3^-1 x √5) } * 6th root of ( 3 x 5^6 ) = 3÷5
Hence proved.
Step-by-step explanation:
olution:
Now, first lets start solving from LHS side, we get :
LHS : { √(3*5^-3) ÷ (∛3^-1 x √5) } * 6th root of ( 3 x 5^6 )
Simplify all the powers, we get:
{ (3 x 5^-3) ^1/2 ÷ (3^-1) ^1/3 (5)^1/2 } x (3 x 5^6)^1/6
{ (3)^1/2 x (5^-3) ^1/2 ÷ (3^-1) ^1/3 (5)^1/2 } x (3 x 5^6)^1/6
Simplifying both the two brackets simultaneously now, we get:
{ (3)^1/2 x (5)^-3/2 ÷ (3) ^-1/3 (5)^1/2 } x ((3)^1/6 x (5)^6/6)
{ (3)^1/2 - (-1/3) x (5)^(-3/2-1/2) } x ((3)^1/6 x (5))
{ (3)^(3+2/6) x (5)^(-4/2) } x ((3)^1/6 x (5))
{ (3)^(5/6) x (5)^(-2) } x ((3)^1/6 x (5))
Now, combining both the brackets together we get:
{ (3)^(5/6 + 1/6) x (5)^(-2 + 1) }
{ (3)^(6/6) x (5)^(-1) }
{ (3)x (5)^(-1) }
{ (3)x (1/5) }
{ 3/5 } ................... RHS
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