Aptitude - Surds and Indices

Answer: Option B

Explanation:

(256)^0.16 x (256)^0.09 = (256)^{(0.16 + 0.09)}

   = (256)^0.25

   = (256)^(25/100)

   = (256)^(1/4)

   = (4⁴)^(1/4)

   = 4^4(1/4)

   = 4¹

   = 4

Answer: Option E

Explanation:

(10)150 ÷ (10)146 =	10150
	10146

   = 10^{150 - 146}

   = 10⁴

   = 10000.

Answer: Option A

Explanation:

Given Exp. =

1  +  1  +  1 1 + xb + xc xa xa 1 + xa + xc xb xb 1 + xb + xa xc xc

=	xa	+	xb	+	xc
	(xa + xb + xc)		(xa + xb + xc)		(xa + xb + xc)

=	(xa + xb + xc)
	(xa + xb + xc)

   = 1.

Answer: Option A

Explanation:

Let (25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^x.

Then,	(52)7.5 x (5)2.5	= 5x
	(53)1.5

	5(2 x 7.5) x 52.5	= 5x
	5(3 x 1.5)

	515 x 52.5	= 5x
	54.5

5^x = 5^{(15 + 2.5 - 4.5)}

5^x = 5¹³

x = 13.

Answer: Option D

Explanation:

(0.04)-1.5 =		4		-1.5
		100

=		1		-(3/2)
		25

   = (25)^(3/2)

   = (5²)^(3/2)

   = (5)^{2 x (3/2)}

   = 5³

   = 125.