( 243 )⁴/₂₅ × ( 243 )¹/₂₅ = ( 243 )⁴/₂₅ ⁺ ¹/₂₅

सही विकल्प: C

( 243 )⁴/₂₅ × ( 243 )¹/₂₅ = ( 243 )⁴/₂₅ ⁺ ¹/₂₅
= ( 243 )⁵/₂₅
= ( 243 )⅕ = ( 3⁵ )⅕ = 3
∴ ( 243 )⁴/₂₅ × ( 243 )¹/₂₅ = 3
अतः इसका मान 3 होगा ।

∵ [ ( x⁻ ³/²⁵ )⁻ ⁵ /³ ]⁵ = ?
⇒ [ ( x⁻ ³/²⁵ )⁻ ⁵ /³ ]⁵ = [ { ( x⁻ ³/²⁵ )⅕ }⁻ ⁵ /³ ]⁵
= x( ⁻ ³/²⁵ )( ⅕ )( ⁻ ⁵ /³ )( ⁵ ) = x

सही विकल्प: C

∵ [ ( x⁻ ³/²⁵ )⁻ ⁵ /³ ]⁵ = ?
⇒ [ ( x⁻ ³/²⁵ )⁻ ⁵ /³ ]⁵ = [ { ( x⁻ ³/²⁵ )⅕ }⁻ ⁵ /³ ]⁵
= x( ⁻ ³/²⁵ )( ⅕ )( ⁻ ⁵ /³ )( ⁵ ) = x
∴ ? = x
अतः इसका मान x होगा ।

∴ ( 243/1024 )⁻ ⁴/⁵ = ( 3⁵/2¹⁰)⁻ ⁴/⁵ = 3⁵ ( ⁻ ⁴/⁵ )/2¹⁰( ⁻ ⁴/⁵ )

सही विकल्प: B

∴ ( 243/1024 )⁻ ⁴/⁵ = ( 3⁵/2¹⁰)⁻ ⁴/⁵ = 3⁵ ( ⁻ ⁴/⁵ )/2¹⁰( ⁻ ⁴/⁵ )
= 3⁻ ⁴/2⁻ ⁸ ⇒ 2⁸/ 3⁴ = 256/81
∴ ( 243/1024 )⁻ ⁴/⁵ = 256/81

∵ ( 64 )¹/⁶ = ?
∴ ( 64 )¹/⁶ = ( 2⁶ )¹/⁶

सही विकल्प: A

∵ ( 64 )¹/⁶ = ?
∴ ( 64 )¹/⁶ = ( 2⁶ )¹/⁶
= 2⁶ × ¹/⁶ = 2
∴ ? = 2

∵ ( 81 )⁷/⁴ = ?
∴ ( 81 )⁷/⁴ = ( 3⁴ )⁷/⁴

सही विकल्प: D

∵ ( 81 )⁷/⁴ = ?
∴ ( 81 )⁷/⁴ = ( 3⁴ )⁷/⁴ = 3⁴ × ⁷/⁴
= 3⁷ = 2187
∴ ? = 2187