1.2.3 Indices, PT3 Practice


Question 10:
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 11:
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 12:
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

Question 13:
Solve:  3 2n+1 = 3 n ×9 ( 9 1 2 ) 3

Solution:
3 2n+1 = 3 n ×9 ( 9 1 2 ) 3 3 2n+1 = 3 n × 3 2 3 3 3 2n+1 = 3 n+2( 3 ) 2n+1=n+5    n=4

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