Exponents Worksheets prevailing makes you familiar with the exponential terms, positive and negative exponents, laws of exponents, radical exponent, etc. Practice different questions to write larger numbers in the short form so that it’s convenient to read and compare. Solve Questions of Exponents provided with Solutions here and understand the approach used to solve various problems. Firstly, try to solve the Problems of Exponents on your own and assess your preparation standards.

1. Evaluate the following

(i) 3^{-3}

(ii) (1/3)^{-4}

(iii) (2/3)^{-2}

(iv) (-5)^{-4}

**Solution:**

(i) 3^{-3}

= (1/3)^{3}

= 1*1*1/3*3*3

= 1/27

(ii) (1/3)^{-4}

= (3)^{4}

= 3*3*3*3

= 81

(iii) (2/3)^{-2}

= (3/2)^{2}

= 3*3/2*2

= 9/4

(iv) (-5)^{-4}

= (1/-5)^{4}

= 1*1*1*1/-5*-5*-5*-5

= 1/ 625

2. Simplify the following

(i) (5/3)^{2} × (4/2)^{2}

(ii) (1/6)^{6} × (3/4)^{-4}

(iii) (1/3)^{-2}× (4/3)^{-3}

(iv) (3/8)^{-3} × (2/4)^{4}

**Solution:**

(i) (5/3)^{2} × (4/2)^{2}

= 25/9*16/4

= 25*16/9*4

= 400/36

= 100/9

(ii) (1/6)^{2} × (3/4)^{-4}

= (1/6)^{2} * (4/3)^{4}

= 1/36*256/81

= 1*256/36*81

= 256/2916

= 64/729

(iii) (1/3)^{-2}× (4/3)^{-3}

= (3/1)^{2}*(3/4)^{3}

= 9/1*27/64

= 9*27/1*64

= 243/64

3. Evaluate

(i) (5/3)^{-2} × (4/5)^{-3} × (2/5)^{0}

(ii) (-2/5)^{-4} × ( -3/5)^{2}

**Solution:**

(i) (5/3)^{-2} × (4/5)^{-3} × (2/5)^{0}

Any number raised to power 0 is 1.

= (3/5)^{2}*(5/4)^{3}*1

= 9/25*125/64*1

= (9*125*1)/25*64*1

= 1125/1600

= 45/64

(ii) (-2/5)^{-4} × ( -3/5)^{2}

= (5/-2)^{4}*( -3/5)^{2}

= 625/16*9/25

= 625*9/16*25

= 5625/400

= 225/16

4. Evaluate

(i) {(-1/3)^{2}}^{-3}

(ii) [{(-4/3)^{2}}^{-3}]^{-1}

(iii) {(3/2)^{-2}}^{1}

**Solution:**

(i) {(-1/3)^{2}}^{-3}

= (-1/3)^{2*-3}

= (-1/3)^{-6}

= (3/-1)^{-6}

= (-3)^{-6}

(ii) [{(-4/3)^{2}}^{-3}]^{-1}

= (-4/3)^{2*-3*-1}

= (-4/3)^{6}

(iii) {(3/2)^{-2}}^{1}

= (3/2)^{-2}

= (2/3)^{2}

5. Simplify the {(1/4)^{-3} – (1/3)^{-3}} ÷ (1/2)^{-3}

**Solution:**

= {(1/4)^{-3} – (1/3)^{-3}} ÷ (1/2)^{-3}

= {(4/1)^{3} – (3/1)^{3}} ÷(2)^{3}

= {64 – 27} ÷ 8

=37/8

6. Evaluate [6^{-1} × 4^{-1}]^{-1} ÷ 3^{-1}]

**Solution:**

= [ 1/6*1/4] ÷ 1/3]

= [1/24] ÷ 1/3

= 1/24*3/1

= 3/24

= 1/8

7. Find the value of x for which (4/3)^{-4} × (4/3) ^{-5} = (4/3)^{3x}?

**Solution:**

(4/3)^{-4} × (4/3) ^{-5} = (4/3)^{3x}

Since bases are equal we need to add the powers

(4/3)^{-4-5} = (4/3)^{3x}

(4/3)^{-9} = (4/3)^{3x}

Equating the terms we can get the value of x as follows

– 9 = 3x

x = -9/3

= -3

8. Evaluate: {(2/3)^{-1} – (1/2)^{-1}}^{-1}

**Solution:**

Given {(2/3)^{-1} – (1/2)^{-1}}^{-1}

= (3/2)^{1} -(1/2)^{-1*-1}

= 3/2 – 1/2

= 2/2

= 1

9. By what number should (-4)^{-1} be multiplied so that the product becomes 36^{-1}?

**Solution:**

(-4)^{-1}*x = 36^{-1}

1/-4*x = 1/36

x = (1/36)/(1/-4)

= 1/36*-4/1

= -4/36

= -1/9

= 9^{-1}

10. If 5^{2x – 1} ÷ 25 = 25, find the value of x?

**Solution:**

5^{2x – 1} ÷ 25 = 25

5^{2x – 1}/25 = 25

5^{2x – 1} = 25*25

5^{2x – 1} = 625

5^{2x – 1} = 5^{4}

2x -1 = 4

2x = 4+1

2x = 5

x = 5/2