Question

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

Answer 1

thanks daddy bot

Answer 2

To apply the properties of integer exponents to generate equivalent expressions, we can use the following rules:

1) a^0 = 1 (any nonzero number raised to the power of zero is equal to 1)
2) a^(-b) = 1/(a^b) (a negative exponent can be rewritten as the reciprocal of the positive exponent)

Now let's apply these rules to the given expression: 4^0 x 5^-2/(-2)^-3.

1) 4^0 is equal to 1, so we can rewrite the expression as 1 x 5^-2/(-2)^-3.

2) 5^-2 can be rewritten as 1/(5^2) and (-2)^-3 can be rewritten as 1/((-2)^3), so the expression becomes 1 x 1/(5^2) / 1/((-2)^3).

Now we can simplify the expression further. In order to divide fractions, we multiply by the reciprocal of the divisor. So the expression becomes:

1 x 1/(5^2) x ((-2)^3)/1.

Simplifying the fractions and exponents, we get:

1 x 1/(25) x (-8) = -8/25.

Therefore, the simplified fraction with no remaining exponents is -8/25.

Answer 3

You're welcome! If you have any more questions, feel free to ask.