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)

Question

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

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 4

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

Answer 5

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).

Answer 6

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

Answer 7

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.