Question

Which of the following is an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?

Answer 1

To apply the Property of Negative Integer Exponents, we can rewrite the expression so that all exponents are positive.

The property states that a^(-n) = 1/(a^n).

Let's use this property to rewrite 25^(-4):

25^(-4) = 1/(25^4)

Now we can substitute this value back into the original expression:

7^3 / 25^(-4) = 7^3 / (1/(25^4))

To divide by a fraction, we can multiply by its reciprocal:

7^3 / (1/(25^4)) = 7^3 * (25^4/1)

The numerator and denominator are both positive exponents now.

Therefore, an equivalent expression with only positive exponents is 7^3 * 25^4.