Which of the following is an equivalent expression to 14^-7/9^-13 with only positive exponents, generated by applying the property of negative integer exponents?
9^13/14^7
1/9^13•14^-7
14^7/9^13
14^-7•9^13
To convert negative exponents to positive exponents, we can use the property that says a^(-n) = 1/a^n.
So, 14^-7/9^-13 = (1/14^7)/(1/9^13).
This is equivalent to: 1/(14^7/9^13).
To divide by a fraction, we can multiply by its reciprocal. Therefore, 1/(14^7/9^13) = 1 * (9^13/14^7).
So, the equivalent expression with only positive exponents is 9^13/14^7.
Therefore, the correct answer is: 9^13/14^7.
To find an equivalent expression with only positive exponents, we can apply the property of negative integer exponents, which states that for any nonzero number a, a^(-n) is equal to 1/a^n.
Starting with the given expression, 14^(-7)/9^(-13), we can rewrite it as:
1/(14^7) * 1/(9^13)
Using the property of negative integer exponents, we can rewrite 14^7 as 1/(14^(-7)) and 9^13 as 1/(9^(-13)), so the expression becomes:
1/(14^(-7)) * 1/(9^(-13))
Now we have the expression with only positive exponents:
1/(14^(-7) * 9^(-13))
Thus, the correct equivalent expression with only positive exponents is:
1/(14^7 * 9^13)
To find an equivalent expression to 14^-7/9^-13 with only positive exponents using the property of negative integer exponents, you need to move the negative exponents to the opposite denominator and change the signs of the exponents.
The property states that a^-n = 1/a^n. So, 14^-7 becomes 1/14^7 and 9^-13 becomes 1/9^13.
Therefore, the equivalent expression is:
1/14^7 / 1/9^13
To divide fractions, you can multiply the first fraction by the reciprocal of the second fraction:
1/14^7 * 9^13/1
Simplifying this expression further, you get:
9^13/14^7
So, the equivalent expression with only positive exponents, generated by applying the property of negative integer exponents, is 9^13/14^7.