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If 1960 = 2a. 5b. 7c, Calculate the Value of 2-a. 7b. 5-c. - Mathematics

Sum

If 1960 = 2a. 5b. 7c, calculate the value of 2-a. 7b. 5-c.

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Solution

1960 = 2a x 5b x 7c
⇒ 2 x 2 x 2 x 5 x 7 x 7 = 2a x 5b x 7c
⇒ 23 x 51 x 72 = 2a x 5b x 7c
⇒  2ax 5b x 7c = 23 x 51 x 72
Comparing powers of 2,5 and 7 on the both sides of equation, We have
a = 3; b = 1 and c = 2
Hence,
Value of 2-a x 7b x 5-c

= 2-3 x 71 x 5-2

= `1/2^3 xx 7 xx 1/5^2`

= `1/8 xx 7 xx 1/[ 5 xx 5 ]`

= `7/200`          

Concept: Laws of Exponents
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 6 | Page 98
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