Indices and Expanding Algebraic Expressions

1.         Simplify m³ ×m⁵                                                          

2.         k⁸ × k⁴ =                                                                                                    
3.         Find the value of ( 3² )²                                                                          

4.         ( – 6n³ )⁴ ÷ (2n²)³ =

5.

6.         Simplify ( 4ac² )³ × 2a^{– 1}                                                                         

7.         Simplify  p¹¹ ÷ ( p⁵ × p ).

8.         Evaluate ( 3^{– 2} )² × 9²                                                             

9.        Given that  3^{2m – 1} = 3⁵, find the value of m.                          

10.       Given that ( 5³ )^x = 5⁹, find the value of x.                            

11.       Expand the following                                                            

           (a)       3(m + 6)                                          
           (b)       – 4 (2 – 3x + 5r)                                                          

12.       Expand the following                                                            

            (a)       (y – 2)(y – 6)                                                  
            (b)       (p + 2)(p – 5)                                     

13.       Expand the following                                                

           (a)       (1 – 4n)²

           (b)       5(2m + 3)^{2
  
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