Use Examples on Exponents during your preparation and understand several questions. The Example Questions provided uses the laws of exponents. We have provided answers to the questions so that you can verify them and analyze where you went wrong. Practice using the Worked Out Examples on Exponents and learn how to solve the related problems.

1. Evaluate the Exponent?

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

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

= (2/1)^{3}

= 8

(ii) (2/5)^{-2}

= (5/2)^{2}

= 25/4

(iii)(-3)^{-5}

= 1/(-3)^{5}

= 1/-3^{5}

= 1/-81

(iv) (-4)^{-3}

= 1/(-4)^{3}

=1/-64

2. Evaluate (-3/7)^{-4} × (-2/3)^{2}?

**Solution:**

Given (-3/7)^{-4} × (-2/3)^{2}

= (7/-3)^{4} × (-2/3)^{2}

= (-7/3)^{4} × (-2/3)^{2}

= -7^{4}/3^{4} *-2^{2}/3^{2}

= (-7^{4}*-2^{2})/3^{4}*3^{2}

=7^{4}*2^{2}/3^{6}

= 9604/729

3. Simplify and find the value of (-1/2)^{-3} × (-1/2)^{-2}?

**Solution:**

Given (-1/2)^{-3} × (-1/2)^{-2}

Since bases are the same the exponents will be added

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

=(-1/2)^{-5}

= (2/-1)^{5}

= -32

4. Evaluate {[(-4)/2]^{3}}^{-4}?

**Solution:**

The given expression is in the form of **(a ^{m})^{n}**

**=**

**a**

^{mn}Therefore, we just have to multiply the powers.

{[(-4)/2]^{3}}^{-4} =(-4/2)^{-12}

= (2/-4)^{12}

5. Simplify (3^{-1} × 4^{-1})^{-1} ÷ 2^{-1}

**Solution:**

= (1/3 ×1/4)^{-1}÷ 2^{-1}

= (3*4)÷1/2

= 12/(1/2)

= 12*2/1

= 24

6. Simplify: (1/4)^{-2} + (1/2)^{-2} + (1/5)^{-2}?

**Solution:**

Given (1/4)^{-2} + (1/2)^{-2} + (1/5)^{-2}

= 4^{2}+2^{2} + 5^{2}

= 16+4+25

= 45

7. By what number should (1/3)^{-1} be multiplied so that the product is (-3/4)^{-1}?

**Solution:**

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

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

= (4/-3)/(3/1)

= 4*3/-3*1

= 12/-3

= -4

8. If a = (3/5)^{2} ÷ (4/5)^{0} find the value of a^{-2}?

**Solution:**

a = (3/5)^{2} ÷ (4/5)^{0}

We know any non zero number raised to the power 0 is 1.

a = (3/5)^{2}÷1

= 9/25÷1

= 9/25

a^{-2} = 1/a^{2}

= 1/(9/25)^{2}

= (25/9)^{2}

= 625/81

9. Find the value of n, when 7^{n} = 343?

**Solution:**

7^{n} = 343

7^{n} = 7^{3}

Since the bases are equal omitting the bases we get the n value i.e. 3.

10. Find the value of n when 81^{2//n} = 9?

**Solution:**

81^{2//n} = 9

(9^{2})^{2/n} = 9

9^{4/n} = 9^{1}

Since the bases are equal, equating the powers we get the value of n as under

4/n = 1

n = 4