which of the following is an equivalent expression to 15^0x7^-2/(-4)^-3 with only the positive exponents that has been generated by applying the properties of integer exponents?

A 7^2/(-4)^3
B 1/7^2x(-4)^-3
C 4^3/7^2
D (-4)^3/7^2

1 answer

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

1. Any non-zero number raised to the power of 0 is equal to 1.
2. To remove a negative exponent, we can move the base to the denominator and change the sign of the exponent.

Let's simplify the expression step by step:

15^0x7^-2/(-4)^-3

First, we can simplify 15^0 and (-4)^-3 as per property 1:

1 x 7^-2 / 1

Next, we can move 7^-2 to the denominator and change the sign of the exponent as per property 2:

1 / (1 x 7^2)

Finally, we can simplify the expression:

1 / 7^2

Therefore, the equivalent expression, with only positive exponents, is Option C: 4^3/7^2.