Question

Mathematics for Class 7
16. Simplify:
16x2n+1 - 4x2n
16x2n+2 - 2x2n+2
17. Find the value of n when:
(i) 5 power 2n x 53 = 59
(iii) 62n+1 = 36 = 6 power 3
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18. If 2n-7 x 5n-4 = 1250, find the value of n.
Hint: 2n-4x2-3x5n-4
2n-4x5n-4
=1250
=1250 = (2x51"-4 = (10)4.
23
EXPRESSING LARGE NUMBERS IN STANDARD FORM
A given number is said to be in standard form if it can be expressed as kx10", whe
real number such that isk<10 and n is a positive integer.
EXAMPLE 22. Express each of the following numbers in standard form:
(i) 270659 (ii) 427500000 (iii) 6830000000
Solution
Each of the given numbers can be expressed in standard form as shown
(ii) 8x2n+2 = 32​

Answer 1

(16*2n+1  -  4*2n) / (16*2n+2  -  2*2n+2)

= (24*2n+1  -  22*2n) / (24*2n+2 -  2*2n+2)        ( by using property  am * an= am+n)

= (24+n+1 - 2n+2) / (24+n+2 - 21+n+2)

= (2n+5-2n+2) / (2n+6-2n+3)

= (2n+2+3-2n+2) / (2n+3+3-2n+3)

= (2n+2)(2n+3-1) / (2n+3)(2n+3-1)

= 2n+2 / 2n+3

= 2n+2-(n+3)                     (by using property  am/an=am-n)

= 2n+2-n-3

= 22-3

= 2-1

=1/2

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