which of the following is equivalent expression to 7^3/25^-4 with only positive exponents generated by applying the properties of negative integer exponents?

Answer 1

To simplify the expression 7^3/25^-4 using properties of negative integer exponents, we can apply the property that states a^(-b) = 1/a^b.

Therefore, we have:

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

Now, let's apply the property a/(1/b) = a*b to simplify further:

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

Finally, using the property a^m * a^n = a^(m+n), we simplify to:

7^(3+4) * 25^4 = 7^7 * 25^4

Thus, the equivalent expression with only positive exponents is 7^7 * 25^4.