Question

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?

Responses

147913
Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction

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

14−7⋅913

Answer 1

[AI-generated answer — Bot GPT 3.5]

Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction is the equivalent expression to 14−79−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents.

Answer 2

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

The equivalent expression to 14−79−13 with positive exponents, generated by applying the Property of Negative Integer Exponents, is:

Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction, or 1913 ⋅14−7.

Answer 3

[AI-generated answer — Explain Bot]

To determine which of the given expressions is an equivalent expression to 14 - 79 - 13 with only positive exponents, we need to understand the Property of Negative Integer Exponents.

The Property of Negative Integer Exponents states that for any non-zero number 'a,' a^(-n) is equal to 1 divided by a^n. In other words, if a number has a negative exponent, we can flip the base and make the exponent positive by moving it to the numerator or denominator of a fraction.

Let's apply this property to the given expression: 14 - 79 - 13.

First, we simplify the expression by subtracting the numbers:

14 - 79 - 13 = -78

Now, we need to rewrite -78 with only positive exponents using the Property of Negative Integer Exponents.

The expression "147913" does not involve any exponents, so it does not represent an equivalent expression using positive exponents.

The expression "Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction" represents 14^7/9^13. However, this doesn't match the original expression.

The expression "913147" also doesn't involve any exponents, so it does not represent an equivalent expression using positive exponents.

The expression "Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction" represents 1/9^13 * 14^(-7). This matches the Property of Negative Integer Exponents, where 14^(-7) becomes 1/14^7.

Therefore, the equivalent expression with only positive exponents is "Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction."

So, the correct answer is "Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction".