(1) `(5x)/(2y^2)*(8x^4)/(5y^2)`

To simplify this expression, we have to multiply the fractions straight across.

=`(5x*8x^4)/(2y^2*5y^2)`

`=(40x*x^4)/(10*y^2*y^2)`

To multiply same base, apply the exponent rule `a^m*a^n=a^(m+n).`

`=(40x^(1+4))/(10y^(2+2))` ` `

`=(40x^5)/(10y^4)`

To simplify this further, cancel the common factor between the numerator and denominator.

`=(4x^5)/y^4`

**Therefore, the simplified form of the given expression is **`(5x)/(2y^2)*(8x^4)/(5y^2) = (4x^4)/y^4.`

(2) `((5x)/(2y^2))/((8x^4)/(5y^2))`

To divide two fractions, take the reciprocal of the second fraction. Change the operation from division to multiplication.

`= (5x)/(2y^2)*(5y^2)/(8x^4)`

Multiply the fractions straight across.

`=(25xy^2)/(16x^4y^2)`

To divide same base, apply the exponent rule `a^m/a^n=a^(m-n).`

`=25/16 x^(1-4)y^(2-2)`

`=25/16x^(-3)y^0`

Take note that when the exponent is zero, it simplifies to 1.

`=25/16x^(-3)*1`

`=25/16x^(-3)`

To express the x with a positive exponent, apply the rule `a^(-m)=1/a^m.`

`=25/16*1/x^3`

`=25/(16x^3)`

**Therefore, the simplified form of the given expression is `((5x)/(2y^2))/((8x^4)/(5y^2))=25/(16x^3).` **