Question

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.

Answer 1

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.