Practice Test on Exponents prevailing will test your conceptual knowledge on Chapter Exponents. Assess your strengths and weaknesses and concentrate on the topics you are lagging accordingly. Try solving the problems on Exponents on your own and verify with the solutions provided. The Questions cover various exponent laws and you can apply them to make your calculations much simple.
1. The Value of (4/5)-2 is
(a) 16/25
(b) 25/2
(c) 25/16
(d) -2/5
Solution:
(a) 16/25
Given Expression is (4/5)-2
= 1/(4/5)2
= (5/4)2
= 25/16
2. The value of (-2)-3 is
(a) -8
(b) 8
(c) -1/16
(d) -1/8
Solution:
(d) -1/8
Given (-2)-3
= (1/-2)3
= (-1/2)3
= (-1/8)
= -1/8
3. What is the value of (-2/5)-2 × (4/3)-3?
(a) -24
(b) – 8192/2187
(c) 675/256
(d) 1/256
Solution:
(c) 675/256
Given (-2/5)-2 × (4/3)-3
= (5/2)2 × (3/4)3
= 25/4*27/64
= (25*27)/(4*64)
= 675/256
4. Find the value of {(2/-3)-2}3 is
(a) -3/2
(b) 4/3
(c) 729/64
(d) 1024/243
Solution:
(c) 729/64
Given {(2/-3)-2}3
= {(-3/2)2}3
= {-3/2}6
= 729/64
5. What is the value of (2-1 + 3-1)-1 ÷ 4-1
(a) 4/10
(b) 10/3
(c) 3/5
(d) 4/15
Solution:
(b) 10/3
Given (2-1 + 3-1)-1 ÷ 4-1
= (1/2+1/3)÷1/4
= ((3+2)/6)÷1/4
= 5/6÷1/4
= 5/6*4/1
= 20/6
= 10/3
6. Simplify: (1/3)-2 + (2/4)-2 + (3/2)-2?
(a) 89/36
(b) 141/36
(c) 21/4
(d) 121/9
Solution:
(d) 121/9
Given (1/3)-2 + (2/4)-2 + (3/2)-2
= (3/1)2+ (4/2)2+(2/3)2
= 9+4+4/9
= (81+36+4)/9
= 121/9
7. The value of x for which (5/12)-4 * (5/12)3x = (5/12)5?
(a) -2
(b) -1
(c) 1
(d) 3
Solution:
(d) 3
(5/12)-4 * (5/12)3x = (5/12)5
Since bases are equal we need to add the powers.
(5/12)-4+3x = (5/12)5
Both the sides are equal and equating the powers we have the value of x as such
-4+3x = 5
3x = 5+4
3x = 9
x = 3
8. If 33x – 1 = 9, then x is equal to
(a) -2
(b) 0
(c) 1
(d) 2
Solution:
(c) 1
33x – 1 = 9
33x/3 = 9
33x = 27
33x = 33
3x = 3
x= 3/3
= 1
9. [{(-1/3)3}-2]-1
(a) 1/15
(b) 23
(c) 729
(d) -15
Solution:
Given [{(-1/3)3}-2]-1
= (-1/3)6
= (3/1)6
= 729
10. {(1/2)-3 – (1/4)-3} ÷ (1/3)-3 = ?
(a) 17/64
(b) 27/16
(c) -56/27
(d) 15/24
Solution:
(c) -56/27
Given {(1/2)-3 – (1/4)-3} ÷ (1/3)-3
= {(2/1)3 -(4/1)3} ÷ (3/1)3
= ((8)-64)÷27
= -56/27