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If 2160 = 2a. 3b. 5c, Find A, B and C. Hence Calculate the Value of 3a X 2-b X 5-c. - Mathematics

Sum

If 2160 = 2a. 3b. 5c, find a, b and c. Hence calculate the value of 3a  x 2-b x 5-c.

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Solution

2160 = 2a x 3b x 5c
⇒ 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 = 2a x 3b x 5c
⇒ 24 x 33 x 51 = 2a x 3b x 5c
⇒ 2a x 3b x 5c = 24 x 33 x 51
Comparing powers of 2, 3 and 5 on the both sides of equation, We have
a = 4; b = 3 and c = 1
Hence,
Value of 3a x 2-b x 5-c
= 34 x 2-3 x 5-1
= 3 x 3 x 3 x 3 x `1/2^3 xx 1/5` 

= `81 xx 1/[ 2 xx 2 xx 2 ] xx 1/5`

= `81 xx 1/8 xx 1/5`

= `81/40`

= `2 1/40`

Concept: Laws of Exponents
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 5 | Page 98
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