Question

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

Answer 1

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.