RD Sharma Solutions - Chapter 2 - Powers (Ex-2.2) Part- 2 Class 8 Math Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 8: By what number should (−5) ⁻¹ be multiplied so that the product is (−8) ⁻¹

Answer 8:
Let the number be x.
According to the question, 

Question 9: By what number should (15) ⁻¹ be multiplied so that the product may be equal to (−5) ⁻¹ ?

Answer 9: 
Let the required number be x.
Therefore,


x=−3
Hence, the required number is −3. 

Question 10:

By what number should (−15)⁻¹ be divided so that the quotient may be equal to (−5)−1?

Answer 10:

Expressing in fractional form, we get:
(−15)⁻¹ = −1/15,      ---> (a⁻¹ = 1/a)
and
(−5)⁻¹ = −1/5           ---> (a⁻¹ = 1/a)
We have to find a number x such that
Solving this equation, we get:                    Hence, (−15)⁻¹ should be divided by 1/3 to obtain (−5)⁻¹.

Question 11:

By what number should (5/3)⁻²  be multiplied so that the product may be (73)⁻¹?

Answer 11:

Expressing as a positive exponent, we have:
        ---> (a−1 = 1/a)                            ---> ((a/b)n = (an)/(bn))                and(7/3)⁻¹ = 3/7.                ---> (a⁻¹ = 1/a)
We have to find a number x such that
Multiplying both sides by 25/9, we get:Hence, (5/3)⁻² should be multiplied by 25/21 to obtain (7/3)⁻¹.

Question 12:

Find x, if


Answer 12:
(i) We have:

                 
   (a^m×aⁿ = a^m+ⁿ)
                                   

x = 3
(ii) We have:

                   
   (a^m×aⁿ = a^m+n)
                                 
                                        

x = 6
(iii) We have:

                     
                               
                                
 
                             

x = 1/2
(iv) We have:

                   
                              
                             
 
                           

x = 10/3
(v) We have:

                 
                     
                             
                                 

(vi) We have:

                 
                       
                                 
 

Question 13:

Answer 13:
(i) First, we have to find x.
x = 322×23-4  = Hence, x⁻² is:

(ii) First, we have to find x.

Hence, the value of x⁻¹ is: