Which of the following is an equivalent expression to 14−79−13
14
−
7
9
−
13
with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
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
Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction
14−7⋅913
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
To find the equivalent expression with only positive exponents, we can apply the Property of Negative Integer Exponents, which states that when a negative exponent appears on a term, we can move it to the denominator by changing its sign to positive.
Therefore, the equivalent expression to 14−79−13 with only positive exponents is:
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
So, the answer is: Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction.
To find the equivalent expression to 14−79−13 using only positive exponents, we need to apply 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, let's break down the expression:
14−79−13
To apply the property of negative exponents, we flip the base if it has a negative exponent. In this case, we need to flip both 79 and 13:
14−7×913
Now, we can rewrite the expression as:
14 × (1/9^7) × (1/9^13)
To simplify further, we can combine the exponents by adding them:
14 × (1/9^(7+13))
Simplifying the exponent:
14 × (1/9^20)
Finally, we have the equivalent expression:
14 × (1/9^20), or as an option presented, 1913 ⋅14−7.