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?
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).