Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 5^−2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

Answer 1

Using the property that any non-zero number raised to the power of 0 is equal to 1 (a^0 = 1), we can simplify 4^0 to 1.

Next, using the property that any number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent (a^(-n) = 1/a^n), we can simplify 5^(-2) to 1/5^2.

And finally, using the property that the reciprocal of any non-zero number raised to the power of -n is equal to the number itself raised to the power of n (1/a^(-n) = a^n), we can simplify (-2)^(-3) to (-2)^3.

So the expression 4^0 ⋅ 5^(-2) / (-2)^(-3) can be simplified to 1 ⋅ 1/(5^2) / (-2)^3
= 1/(25) / (-8)
= 1/25 / -8
= 1/25 * (-1/8)
= -1/200