If \(5\sqrt5\times5^3÷5^{-\frac32} = 5^{a+2}\), then the value of a

1.	If \(5\sqrt5\times5^3÷5^{-\frac32} = 5^{a+2}\), then the value of a is(a) 4 (b) 5 (c) 6 (d) 8
Answer» (a) 4 \(5\sqrt5\times5^3÷5^{-\frac32} = 5^{a+2}\) ⇒ \(5^{\frac32}\times5^3÷5^{-\frac32} = 5^{a+2}\) ⇒ \(5^{\frac32+3-(-\frac32)} = 5^{a+2}\) ⇒ 5⁶ = 5^a+2 ⇒ a + 2 = 6 ⇒ a = 4

If \(5\sqrt5\times5^3÷5^{-\frac32} = 5^{a+2}\), then the value of a is(a) 4 (b) 5 (c) 6 (d) 8

Answer»

(a) 4

\(5\sqrt5\times5^3÷5^{-\frac32} = 5^{a+2}\)

⇒ \(5^{\frac32}\times5^3÷5^{-\frac32} = 5^{a+2}\)

⇒ \(5^{\frac32+3-(-\frac32)} = 5^{a+2}\)

⇒ 5⁶ = 5^a+2 ⇒ a + 2 = 6 ⇒ a = 4