Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 (−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

Responses

7^2\(−4)^3

(−4)^3\7^2

1\7^2 ⋅ (−4)^−3

4^3\7^2

1 answer

To simplify the expression, we can use the properties of exponents.

First, we know that any number raised to the power of 0 is equal to 1. So, 15^0 is equal to 1.

Next, we can rewrite 7^(-2) as 1/7^2. The negative exponent indicates that we need to take the reciprocal of the base.

Similarly, (-4)^(-3) can be rewritten as 1/(-4)^3.

Combining these simplifications, we get:

15^0 * 7^(-2) * (-4)^(-3)
= 1 * 1/7^2 * 1/(-4)^3
= 1/7^2 * 1/(-64)
= 1/49 * 1/(-64)
= 1/(49 * -64)

So, the equivalent expression with positive exponents is 1/(49 * -64), which is not one of the given options.