Question

Which of the following is an equivalent expression to 13^−5 ⋅ 13^−11 with only positive exponents, generated by applying the properties of exponents?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the expression using the properties of exponents, we can first combine the bases of the two exponentials since they are the same. When we multiply two numbers with the same base, the exponents are added. Therefore:

13^(-5) ⋅ 13^(-11) = 13^(-5-11)

= 13^(-16)

To convert the expression to positive exponents, we can use the property that a negative exponent is equal to the reciprocal of the positive exponent. Therefore:

13^(-16) = 1 / 13^(16)

So the equivalent expression with only positive exponents is 1 / 13^(16).

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression, 13^−5 ⋅ 13^−11, with only positive exponents, we can use the property of exponents that states:

a^m ⋅ a^n = a^(m + n)

So, by applying this property, we can add the exponents:

13^(-5) ⋅ 13^(-11) = 13^((-5) + (-11))

Simplifying further:

13^(-5) ⋅ 13^(-11) = 13^(-16)

Therefore, an equivalent expression with only positive exponents is 13^(-16).