^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)

Question

4^0 ⋅ 5^−2/(−2)^−3=

Answer 1

4^0 ⋅ 5^−2/(−2)^−3 = 1 ⋅ (1/5^2) / (1/(-2)^3)

Using the property (a/b)^n = (a^n)/(b^n),
= 1 ⋅ 1/(5^2) / 1/(-8)

Using the property a/b = a ⋅ 1/b,
= 1/(5^2) ⋅ (-8)

Simplifying further,
= 1/25 ⋅ (-8)

Multiplying,
= -8/25

Therefore, the expression simplifies to -8/25.

Answer 2

Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(14^3⋅27^−7)^0/3^4=

Answer 3

(14^3⋅27^−7)^0/3^4 = 1/3^4

Using the property (a^m)^n = a^(m*n),
= (14^3)^(0/1) ⋅ (27^−7)^(0/1) / (3^4)^(0/1)

Using the property a^0 = 1,
= (1) ⋅ (1) / (1)

Therefore, the expression simplifies to 1/1, which is equal to 1.