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

To eliminate negative exponents, we can use the property that states "a^(-b) = 1/a^b".

So, we can rewrite the expression as:

4^0 * 5^(-2) / (-2)^(-3)

Since any number (except 0) raised to the power of 0 is equal to 1, 4^0 equals 1.

So, the expression becomes:

1 * 5^(-2) / (-2)^(-3)

Now, let's evaluate the exponents:

5^(-2) = 1 / 5^2 = 1 / 25

(-2)^(-3) = 1 / (-2)^3 = 1 / (-8) = -1/8

Substituting these values back into the expression, we have:

1 * 1/25 / (-1/8)

To divide fractions, we invert the second fraction and multiply:

1 * 1/25 * (-8/1) = (-8)/(25)

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