Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0.5^-2/(-2)-3 with only one positive exponents, then solve the expression. your answer will be simplified with no remaining exponents.
To generate equivalent expressions with only one positive exponent, we can use the property that states: a^(-b) = 1/a^b.
Starting with the expression 4^(0.5^(-2))/(-2)^(-3), we can apply the property to change the negative exponents into positive ones:
= 4^((0.5^2))/((-2)^3)
= 4^(0.25)/(8)
= √4/8
= 2/8
Now, we can simplify the expression by dividing numerator and denominator by their greatest common factor, 2:
= 1/4
Therefore, the simplified expression is 1/4.