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

Using the properties of integer exponents, we can simplify the expression:

4^0 ⋅ 5^−2\(−2)^−3

Since any number raised to the power of 0 is equal to 1, we can simplify 4^0 to 1:

1 ⋅ 5^−2\(−2)^−3

To remove the negative exponents, we can use the property of negative exponents which states that a^−b is equivalent to 1/a^b:

1 ⋅ 1/5^2 \ 1/(-2)^3

Since any number raised to the power of a negative exponent is equivalent to the reciprocal of that number raised to the positive exponent, we can simplify 1/5^2 to 1/25:

1/25 \ 1/(-2)^3

Now, let's simplify the expression (-2)^3:

1/25 \ -8

Finally, let's combine the fractions by multiplying -8 by the reciprocal of 25:

-8/25

Answer 2

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.
4^0 ⋅ 5^−2\(−2)^−3=

Answer 3

Using the properties of integer exponents, we can simplify the expression:

4^0 ⋅ 5^−2\(−2)^−3

Since any number raised to the power of 0 is equal to 1, we can simplify 4^0 to 1:

1 ⋅ 5^−2\(−2)^−3

To remove the negative exponents, we can use the property of negative exponents which states that a^−b is equivalent to 1/a^b:

1 ⋅ 1/5^2 \ 1/(-2)^−3

Now, let's simplify the expression 1/5^2:

1/(5^2) \ 1/(-2)^−3

Since 5^2 is equal to 25, we can simplify 1/(5^2) to 1/25:

1/25 \ 1/(-2)^−3

Now let's simplify the expression 1/(-2)^−3:

1/25 \ 1/((-2)^3)

Since (-2)^3 is equal to -8, we can simplify 1/(-2)^−3 to 1/(-8):

1/25 \ 1/(-8)

Finally, let's simplify the expression 1/(-8):

1/25 \ -1/8

Therefore, the equivalent expression in positive exponents is:
4^0 ⋅ 5^−2\(−2)^−3 = -1/8