Which of the following is an equivalent expression to 13^−5 ⋅13^−11 with only positive exponents, generated by applying the properties of exponents?(1 point)
Responses
1/2666
Start Fraction 1 over 26 superscript 6 baseline end fraction
1/26^16
Start Fraction 1 over 26 superscript 16 baseline end fraction
1/13^6
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
11/3^16
To simplify the expression 13^−5 ⋅13^−11 with positive exponents, we can use the property of exponents which states that a^(-b) = 1/a^b.
Using this property, we can rewrite the expression as:
1/(13^5) ⋅ 1/(13^11)
Now, using the property of exponents which states that a^b ⋅ a^c = a^(b+c), we can simplify further:
1/(13^(5+11))
1/13^16
Therefore, the equivalent expression with positive exponents is 1/13^16.
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
1/9^13 ⋅14^−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
14^−7⋅9^13
14 superscript negative 7 baseline times 9 superscript 13 baseline
14^7/9^13
Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction
9^13/14^7
To simplify the expression 14^−7/9^−13 with positive exponents, we can apply the property of negative integer exponents which states that a^(-b) = 1/a^b.
Using this property, we can rewrite the expression as:
1/(14^7) ⋅ 1/(9^(-13))
Now, using the property of negative exponents which states that 1/a^(-b) = a^b, we can simplify further:
1/(14^7) ⋅ 9^13
Therefore, the equivalent expression with positive exponents is 9^13/14^7.
Which of the following is an equivalent expression to 7325−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
73254
Start Fraction 7 cubed over 25 superscript 4 baseline end fraction
73⋅254
7 cubed times 25 superscript 4 baseline
2547−3
Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction
25473
To simplify the expression 7325−4 with positive exponents, we can apply the property of negative integer exponents which states that a^(-b) = 1/(a^b).
Using this property, we can rewrite the expression as:
1/(732^4)
Therefore, the equivalent expression with positive exponents is 1/(732^4).
Which of the following is an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
73254
Start Fraction 7 cubed over 25 superscript 4 baseline end fraction
73⋅254
7 cubed times 25 superscript 4 baseline
2547−3
Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction
25^4/7^3
To simplify the expression 7^3/25^−4 with positive exponents, we can apply the property of negative exponents which states that a^(-b) = 1/(a^b).
Using this property, we can rewrite the expression as:
7^3/(1/25^4)
Now, using the property of dividing fractions which states that a/(1/b) = a * b, we can simplify further:
7^3 * 25^4
Therefore, the equivalent expression with positive exponents is 7^3 * 25^4.