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?

Question

Responses

14^−7⋅9^13

9^13/14^7

1/9^13 ⋅14^−7

14^7/9^13

Answer 1

The correct equivalent expression with only positive exponents, generated by applying the Property of Negative Integer Exponents, is 9^13/14^7.

Answer 2

can you explain

Answer 3

Certainly! To convert an expression with negative exponents into one with positive exponents, we can apply the Property of Negative Integer Exponents, which states that a number raised to a negative exponent can be rewritten as 1 divided by the number raised to the positive value of the exponent.

In this case, we have 14^−7/9^−13. To convert the negative exponents to positive exponents, we can rewrite the expression using the Property of Negative Integer Exponents.

For 14^−7, we can rewrite it as 1 divided by 14^7. This is because the negative exponent -7 becomes positive when we apply the property.

Similarly, for 9^−13, we rewrite it as 1 divided by 9^13.

So now our expression becomes:

1/14^7 divided by 1/9^13.

To divide by a fraction, we can multiply by the reciprocal. So our expression becomes:

1/14^7 multiplied by 9^13/1.

Simplifying this expression, we get:

9^13/14^7.

Therefore, the equivalent expression to 14^−7/9^−13 with only positive exponents is 9^13/14^7.