Apply the property of integer exponents to generate equivalent expression to 4^.5^-2/(-2)^-3with only positive exponents then solve the expression. Your answer will be a simplified fraction with no remaining exponents
To apply the property of integer exponents, we can rewrite the expression using the rule: (a^m)^n = a^(m*n).
First, let's rewrite the base 4 as (2^2) to get:
(2^2)^(0.5^(-2))/(2^(-2))^(-3)
Using the property of exponents above, we can simplify further:
2^(2*0.5^(-2))/(2^(-6))
Now, applying the property of exponent division, we subtract the exponents:
2^(2*(0.5^(-2)+6))
Next, simplify:
2^(2*(0.5^(-2)+6)) = 2^(12+2*(0.5^(-2)))
Finally, evaluate the expression:
2^(12+2*(0.5^(-2))) = 2^(12+2*(4))
= 2^(12+8)
= 2^20
Therefore, the simplified fraction with no remaining exponents is 2^20.