Which of the following is an equivalent expression to 14−79−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
14−7⋅913
14 superscript negative 7 baseline times 9 superscript 13 baseline
913147
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction
1913 ⋅14−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
147913
The correct answer is:
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction
The equivalent expression to 14−79−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents, is 913147.
To find the equivalent expression with only positive exponents, we need to apply the Property of Negative Integer Exponents. According to this property, any term with a negative exponent can be rewritten as the reciprocal of the term with the corresponding positive exponent.
In the given expression, we have 14^-7 * 9^-13. To apply the property, we will rewrite 14^-7 as 1/14^7 and 9^-13 as 1/9^13.
Therefore, the equivalent expression with only positive exponents is (1/14^7) * (1/9^13), which can also be written as (1/9^13) * (1/14^7).
So, the correct option is 1/9^13 * 1/14^7.