Question

calculate the value of m+n+p if 2^m×3^n×7^p=21168​

Answer 1

I think your question is -> if 2^m . 3^n . 7^p = 21168 , find the values of m , n and p and also find the value of 5^m . 2^n . p^4 , right ?

first of all, we have to find prime factors of 21168.

i.e., 21168 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7

= 2⁴ × 3³ × 7²

but given, 21168 = 2^m . 3^n . 7^p

so, 2⁴ . 3³ . 7² = 2^m . 3^n . 7^p

on comparing we get,

m = 4 , n = 3 and p = 2

now, 5^m . 2^n . p^4 = 5⁴ . 2³ . 2⁴

= (625) . (8) . (16)

= 80,000

hence, value of 5^m . 2^n . p^4 = 80,000

Answer 2

Answer:

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