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 generate an equivalent expression with only positive exponents, we can use the property that states that any number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent.
Applying this property to the given expression, we can rewrite it as:
4^(0.5^(-2))/(-2)^(-3)
Now, let's simplify each exponent:
0.5^(-2) = 1/(0.5^2) = 1/0.25 = 4
(-2)^(-3) = 1/((-2)^3) = 1/(-8) = -1/8
Now, substitute these values back into the expression:
4^4/(-1/8)
Now, let's simplify the numerator:
4^4 = 4 * 4 * 4 * 4 = 256
Substituting this value back into the expression:
256/(-1/8)
To divide by a fraction, we multiply by its reciprocal:
256 * (-8/1)
This results in:
-2048
Therefore, the simplified fraction with no remaining exponents is: -2048.