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?(1 point)
responses
14^7/9^13
14^-7 ⋅ 9^13
1/9^13⋅14^-7
9^13/14^7
The correct equivalent expression, generated by applying the Property of Negative Integer Exponents, is 9^13/14^7.
To convert the expression 14^-7/9^−13 to an equivalent expression with only positive exponents, we can use the Property of Negative Integer Exponents, which states that a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.
So, the equivalent expression is 14^-7 ⋅ 9^13.
Therefore, the correct answer is (2) 14^-7 ⋅ 9^13.
To find the equivalent expression with only positive exponents, we can apply the Property of Negative Integer Exponents, which states that for any non-zero number a, a^(-n) is equal to 1/a^n.
Start with the given expression: 14^-7/9^(-13).
Apply the Property of Negative Integer Exponents to both the numerator and denominator:
14^-7 becomes 1/14^7.
9^(-13) becomes 1/9^13.
So the expression becomes: (1/14^7)/(1/9^13).
Next, when dividing fractions, we invert the second fraction and multiply:
(1/14^7) * (9^13/1).
Simplify the expression:
9^13/14^7.
Therefore, the correct answer is: 9^13/14^7.