If a=2^p ×3^q × 5^rand b= p²× q³ × r⁵, where p,q and r are primes, find the value of p+q+r , given that a=b.

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Solution

In question, it is given a=b
Just look at a and b.

if p=2 q=3 r=5

then a=2^2 × 3^3 ×5^5

and also
b= 2^2 × 3^3 ×5^5.

so they becomes equal.
so we understand that possible value of p,q,r are 2,3,5 respectively.

so p+q+r =2+3+5=10.

like if satisfied

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If a=2p ×3q × 5r and b= p​​​​​​2 × q​​​​​​3 × r​​​​​​5 , where p,q and r are primes, find the value of p+q+r , given that a=b.

In question, it is given a=b Just look at a and b. if p=2 q=3 r=5 then a=2^2 × 3^3 ×5^5 and also b= 2^2 × 3^3 ×5^5. so they becomes equal. so we understand that possible value of p,q,r are 2,3,5 respectively. so p+q+r =2+3+5=10. like if satisfied

If a=2^p ×3^q × 5^rand b= p²× q³ × r⁵, where p,q and r are primes, find the value of p+q+r , given that a=b.

In question, it is given a=b
Just look at a and b.

if p=2 q=3 r=5

then a=2^2 × 3^3 ×5^5

and also
b= 2^2 × 3^3 ×5^5.

so they becomes equal.
so we understand that possible value of p,q,r are 2,3,5 respectively.

so p+q+r =2+3+5=10.

like if satisfied