Simplify the expression and eliminate any negative exponents

Simplify the expression and eliminate any negative exponent(s). Assume that s denotes a positive number.

s^7/2(2s ^ 7/4)^2 / s^1/2

s^7/2(2s^7/4)²/s^1/2

law of exponents: (ab)^m=a^mb^m

s^7/2(2²)(s^7/4)²/s^1/2

law of exponents: (a^m)ⁿ=a^mn

=s^7/2(2²)(s⁽^7/4)*2)/s^1/2

=s^7/2(4)(s⁽^7/2))/s^1/2

=4s^7/2s^7/2/s^1/2

law of exponents:a^m*aⁿ=a^m+n

=4s⁽^7/2)+⁽^7/2)/s^1/2

=4s⁷/s^1/2

law of exponents:a^m/aⁿ=a^m-n

=4s^7-(1/2)

=4s^13/2

s^7/2(2s^7/4)²/s^1/2=4s^13/2