model 3 based on positive and negative exponent Practice Questions Answers Test with Solutions & More Shortcuts

Answer:(c)

$3^{2x - y} = 3^{x + y} = √27 = (3)^{3/2}$

2x - y = $3/2$

4x - 2y = 3 ....(i)

and, $3^{x + y} = (3)^{3/2}$

x + y = $3/2$

2x + 2y = 3 ....(ii)

From equations (i) and (ii)

4x - 2y + 2x + 2y = 3 + 3

6x = 6 ⇒ x = 1

From equation (i),

4 - 2y = 3

2y = 1 ⇒ $y = 1/2$

$3^{x - y} = 3^{1- 1/2}$ = √3$

Answer:(d)

$(3 +2√2)^{-3}+ (3 -2√2)^{- 3}$

$(3 + 2√2) (3 - 2√ 2)$

= $(3)^2 - (2√2)^2$ = 9 - 8 = 1

$3 + 2√2 = 1/{3 - 2√2}$

$(x + y)^3 + (x - y)^3 = x^3 + y^3 + 3x^2 y + 3 x y^2 + x^3 - y^3 - 3 x^2 y + 3 x y^2$

= $2 x^3 + 6 x y^2$

$(3 + 2√2 )^{ - 3} + (3 - 2√2)^{ - 3}$

= $(1/{3 + 2√2})^3 +(1/{3 -2√2})^3$

= $(3 - 2√2)^3 + (3 + 2√2)^3$

= $2 × (3)^3 + 6 × 3 × (2√2)^2$

= 2 × 27 + 18 × 8

= 54 + 144 = 198

Answer:(d)

$(2000)^10 = 1.024 × 10^k$

$(2×10^3)^10=1024/1000×10^k$

$2^10×10^30=1024×10^{k-3}$

$2^10×10^30=2^10×10^{k-3}$

30 = k - 3 ⇒ k = 33

Answer:(d)

$(8/125)^{-4/3}=(2^3/5^3)^{-4/3}$

=$[(2/5)^3]^{-4/3}=(2/5)^{-4/3×3}$

=$(5/2)^4=625/16$

Answer:(a)

$x +1/x$= 2

${x^2 +1}/x= 2$

$x^2 + 1 = 2x$

$x^2$ - 2x + 1 = 0

$(x - 1)^2$ = 0

x - 1 = 0

x = 1

$x^99 + 1/x^99 - 2$ = 1 + 1 - 2 = 0