model 3 based on positive and negative exponent Practice Questions Answers Test with Solutions & More Shortcuts
power, indices and surds PRACTICE TEST [5 - EXERCISES]
model 1 find largest and smallest value
model 2 based on simplification
model 3 based on positive and negative exponent
model 4 simplifying roots with values
model 5 simplifying roots of roots
Question : 21 [SSC CGL Tier-I 2014]
If $5√5 ×5^3 ÷5^{-3/2}= 5^{a+2}$, then the value of a is
a) 5
b) 8
c) 6
d) 4
Answer »Answer:(d)
$5√5 ×5^3 ÷5^{-3/2}= 5^{a+2}$
$5 × 5^{1/2} × 5^3 ÷ 5^{-3/2} = 5^{a + 2}$
$5^{1+ 1/2 +3+ 3/2} = 5^{a + 2}$
$5^6 = 5^{a + 2}$ ⇒ a + 2 = 6
a = 6 - 2 = 4
$[a^m × a^n = a^{m + n},]$
$[a^m ÷ a^n = a^{m - n}]$
Question : 22
If $(2^3)^2= 4^x$ then $3^x$ is equal to
a) 6
b) 27
c) 9
d) 3
Answer »Answer:(b)
$(2^3)^2=(2^2)^x$
$2^6 = 2^{2x}$ ⇒ 2x = 6
$x = 6/2$ = 3
$3^x = 3^3 = 3 × 3 × 3 = 27$
Question : 23
Simplify : $[√^3{√^6{√{5^9}}}]^4[√^3{√^6{√{5^9}}}]^4$
a) $5^4$
b) $5^12$
c) $5^8$
d) $5^2$
Answer »Answer:(a)
$[√^3{√^6{√{5^9}}}]^4[√^3{√^6{√{5^9}}}]^4$
=$[5^{9×1/6×1/3}]^4[5^{9×1/6×1/3}]^4$
=$[5^{1/2×4}][5^{1/2×4}]=5^2×5^2=5^4$
Question : 24 [SSC CGL Tier-I 2014]
Solve for x : $3^x - 3^{x - 1}$ = 486.
a) 9
b) 6
c) 5
d) 7
Answer »Answer:(b)
$3^x - 3^{x - 1} = 486$
$3^{x - 1}$(3 - 1) = 486
$3^{x - 1}$ × 2 = 486
$3^{x - 1} = 486/2$ = 243
$3^{x - 1} = 3^5$ ⇒ x - 1 = 5
x = 5 + 1 = 6
Question : 25
If $2^{x - 1} + 2^{x + 1}$ = 320, then the value of x is
a) 8
b) 7
c) 5
d) 6
Answer »Answer:(b)
$2^{x - 1} + 2^{x + 1}$ = 320
$2^{x-1}(1+ 2^2) = 320$
$2^{x-1} ×5 =320$
$2^{x-1}= 320/5 =64 ⇒2^{x -1} = 2^{6}$
$x - 1 = 6 ⇒ x = 7$
IMPORTANT quantitative aptitude EXERCISES
model 3 based on positive and negative exponent Shortcuts »
Click to Read...model 3 based on positive and negative exponent Online Quiz
Click to Start..power, indices and surds Shortcuts and Techniques with Examples
-
model 1 find largest and smallest value
Defination & Shortcuts … -
model 2 based on simplification
Defination & Shortcuts … -
model 3 based on positive and negative exponent
Defination & Shortcuts … -
model 4 simplifying roots with values
Defination & Shortcuts … -
model 5 simplifying roots of roots
Defination & Shortcuts …
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