if a/b=c/d=e/f then find the value of 2a^4b^2+3a^2 c^2-5e^4f/(upon) 2b^6+3b^2 d^2-5f^5 in terms of a and b.

To find the value of the expression in terms of a and b, we need to simplify it by substituting the given equation:

a/b = c/d = e/f = k (let's say)

Therefore, we can rewrite the expression as follows:

2a^4b^2 + 3a^2c^2 - 5e^4f / (2b^6 + 3b^2d^2 - 5f^5)

= 2a^4b^2 + 3a^2(kb)^2 - 5(kb)^4 / (2b^6 + 3b^2(kd)^2 - 5(kf)^5)

= 2a^4b^2 + 3a^2k^2b^2 - 5k^4b^4 / (2b^6 + 3b^2k^2d^2 - 5k^5f^5)

Now, we need to simplify the expression further. Since a/b = c/d = e/f = k, we can substitute these values:

= 2a^4b^2 + 3a^2k^2b^2 - 5k^4b^4 / (2b^6 + 3b^2k^2d^2 - 5k^5f^5)

= 2a^4b^2 + 3a^2k^2b^2 - 5k^4b^4 / (2b^6 + 3b^2k^2d^2 - 5k^5(kf)^5)

Since a/b = c/d = e/f = k, we can simplify further:

= 2a^4b^2 + 3a^2k^2b^2 - 5k^4b^4 / (2b^6 + 3b^2k^2d^2 - 5k^10f^5)

Therefore, the simplified expression in terms of a and b would be:

(2a^4b^2 + 3a^2k^2b^2 - 5k^4b^4) / (2b^6 + 3b^2k^2d^2 - 5k^10f^5)