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
1913 ⋅14−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
147913
Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction
14−7⋅913
14 superscript negative 7 baseline times 9 superscript 13 baseline
913147
The correct answer is: $14^{-7} \cdot 9^{13}$
The equivalent expression with only positive exponents, generated by applying the Property of Negative Integer Exponents, is:
14^7/9^13
To find an equivalent expression to 14−79−13 with only positive exponents using the Property of Negative Integer Exponents, we can use the following rule:
For any non-zero number a, a raised to the negative exponent -n is equal to 1 divided by a raised to the positive exponent n. In other words, a^(-n) = 1 / a^n.
Now let's apply this rule to the expression 14−79−13:
14−79−13 = 1 / 14^7 / 9^13
Simplifying further, we can combine the denominators:
14−79−13 = 1 / (14^7 * 9^13)
Therefore, the equivalent expression with only positive exponents is option:
Start Fraction 1 over 14^7 * 9^13 End Fraction