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

Answer:(b)

$x^2 - √3$ = 0

$x^2-(3)^{1/2}=0$

$x^2-(3^{1/4})^2=0$

$(x+3^{1/4})(x-3^{1/4})=0$

$x=3^{1/4} or {-3}^{1/4}$

Product of roots

$=3^{1/4}×-3^{1/4}=-√3$

Note : Product of the roots of $ax^2+bx+c=0 is c/a$

Product of the roots of $x^2-b. 0-√3=0 is -√3$

Answer:(c)

$(3/4)^×3(4/3)^{-7}= (3/4)^{2x}$

$(3/4)^3×(3/4)^{7}= (3/4)^{2x}$

$(3/4)^10=(3/4)^{2x}$

2x=10⇒ x=5

Answer:(b)

Expression = $(10)^100/(5)^75$

= $(2×5)^100/(5)^75$

= ${(2)^100 × (5)^100}/(5)^75$

= $2^100× 5^25$

= $2^25× 5^25× 2^75$

= $(10)^25 ×2^75$

Answer:(c)

Expression

= $[(0.87)^2 + (0.13)^2 + 0.87 × 0.26]^2013$

= $(0.87 + 0.13)^{2013} = 1^{2013}$ = 1

[Since, $(a + b)^2 = a^2 + b^2$ + 2ab]

Answer:(d)

a = $(b)^p$ and b = $(c)^q$

$c = a^r = (b^p)^r = (b)^{pr}$

= $(c^q)^{pr} = c^{pqr}$

pqr = 1