Question

Prove that:- (Question in attachment)

Answer 1

To prove -

( 64/125 ) ^ ( -2/3) + 1 / ( 256/625 ) ^ ( 1/4) + ( √25/3√64 )^0 = 61/16

LHS -

⇢ ( 64/125 ) ^ ( -2/3) + 1 / ( 256/625 ) ^ ( 1/4) + ( √25/3√64 )^0

⇢( 4^3/5^3 ) ^ ( -2/3) + 1 / ( 4^4/5^4 ) ^ ( 1/4) + 1

⇢( 4/5 ) ^ (3×-2/3) + ( 5/4 ) ^ (4× 1/4) + 1

⇢( 4/5 ) ^ (3×-2/3) + ( 5/4 ) ^ (4× 1/4) + 1

⇢( 4/5 ) ^ -2 + ( 5/4 ) ^ 1+ 1

⇢( 25/16 ) + ( 5/4 ) + 1

⇢ 25 + 20 + 16 / 16 [LCM = 16]

⇢ 61 / 16

RHS -

⇢ 61/16

Now we can see that , LHS = RHS

Hence proved !

Answer 2

Step-by-step explanation:

Answer is in attachment