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

Answer 1

To simplify the expression and remove the negative exponents, we can apply the properties of integer exponents:

First, as any number raised to the power of 0 is equal to 1, 15^0 is equal to 1.

Next, we can rewrite 7^−2 as 1/7^2, since a negative exponent denotes the reciprocal of the base raised to the positive exponent.

Similarly, (−4)^−3 can be rewritten as 1/(−4)^3, using the same logic.

Now our expression becomes:
1 * 1/7^2 * 1/(−4)^3

To simplify further, we can apply the power of a product property, which states that (a * b)^n = a^n * b^n:

1 * 1/49 * 1/−64

To simplify further, we multiply the fractions:

1/49 * 1/−64 = 1/(-3136)

Therefore, an equivalent expression to 15^0 X 7^−2 / (−4)^−3 with only positive exponents is 1/(-3136).