5.2.2 Indices, PT3 Practice


Question 8:
Given that 2 8x =32 , calculate the value of x.

Solution:
2 8x =32 2 8x =2 5 8x=5 x=3 x=3


Question 9:
Given  3 2p1 =( 3 p )( 3 2 ), calculate the value of p.

Solution:
3 2p1 =( 3 p )( 3 2 ) 3 2p1 = 3 p+2 2p1=p+2 p=3


Question 10:
Given that 8× 8 p+1 =( 8 5 )( 8 3 ), find the value of p.

Solution:
8× 8 p+1 =( 8 5 )( 8 3 ) 8 1+p+1 = 8 5+3 2+p=8 p=6


Question 11:
Given that  2 5 × 2 7 2 10 = 2 p , find the value of p.

Solution:
2 5 × 2 7 2 10 = 2 p 2 5+710 = 2 p 2 2 = 2 p p=2


Question 12:
Simplify:  12 p 10 q 6 3 p 4 q 2 × ( 4p q 3 ) 2

Solution:
12 p 10 q 6 3 p 4 q 2 × ( 4p q 3 ) 2 = 12 p 10 q 6 3 p 4 q 2 ×16 p 2 q 6                           = 12 1 p 1042 q 626 3 1 × 16 4                           = p 4 q 2 4                           = p 4 4 q 2


Question 13:
Simplify:  a b 2 × ( 8 a 3 b 6 ) 1 3 ( a 2 b 4 ) 1 2

Solution:
a b 2 × ( 8 a 3 b 6 ) 1 3 ( a 2 b 4 ) 1 2 = a b 2 ×( 8 1 3 a 3 ( 1 3 ) b 6( 1 3 ) ) a 2( 1 2 ) b 4( 1 2 )                        = a b 2 ×2a b 2 a b 2                        =2a b 2

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