Question

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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

According to the Property of Negative Integer Exponents, $a^{-n}=\frac{1}{a^n}$ for any nonzero number $a$. Therefore, $14^{-7}=\frac{1}{14^7}$ and $9^{-13}=\frac{1}{9^{13}}$. So, \[14^{-7}/9^{-13}=\frac{1}{14^7}/\frac{1}{9^{13}}=\frac{1}{14^7}\cdot\frac{9^{13}}{1}\]Therefore, we can have an equivalent expression with only positive exponents by moving both 9 and 1 to the numerator: \[\frac{9^{13}}{14^7}\]Thus, the expression $\boxed{\frac{9^{13}}{14^7}}$ is equivalent to $14^{-7}/9^{-13}$ with only positive exponents.

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

Answer 3

[AI-generated answer — Bot GPT 3.5]

According to the Property of Negative Integer Exponents, $a^{-n}=\frac{1}{a^n}$ for any nonzero number $a$. Applying this property to $14^{-7}$ and $9^{-13}$, we have $14^{-7}=\frac{1}{14^7}$ and $9^{-13}=\frac{1}{9^{13}}$.

The expression $14^{-7}/9^{-13}$ can then be rewritten as $\frac{\frac{1}{14^7}}{\frac{1}{9^{13}}}$. To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the expression as $\frac{1}{14^7} \cdot \frac{9^{13}}{1}$.

Finally, we can simplify the expression by moving the denominator $14^7$ to the numerator. This gives us $\frac{9^{13}}{14^7}$.

Therefore, the expression $\boxed{\frac{9^{13}}{14^7}}$ is an equivalent expression to $14^{-7}/9^{-13}$ with only positive exponents.

Answer 4

are you sure

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake. Let's reconsider the expression $14^{-7}/9^{-13}$ using the Property of Negative Integer Exponents.

According to the property, $a^{-n}=\frac{1}{a^n}$ for any nonzero number $a$. Applying this property to $14^{-7}$ and $9^{-13}$, we have $14^{-7}=\frac{1}{14^7}$ and $9^{-13}=\frac{1}{9^{13}}$.

The expression $14^{-7}/9^{-13}$ can then be rewritten as $\frac{\frac{1}{14^7}}{\frac{1}{9^{13}}}$. To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the expression as $\frac{1}{14^7} \cdot \frac{9^{13}}{1}$.

In this form, we have two fractions being multiplied. To multiply fractions, we multiply the numerators together and the denominators together. Therefore, we have $\frac{1}{14^7} \cdot \frac{9^{13}}{1}=\frac{1\cdot 9^{13}}{14^7\cdot 1}=\boxed{\frac{9^{13}}{14^7}}$.

So the expression $\boxed{\frac{9^{13}}{14^7}}$ is indeed an equivalent expression to $14^{-7}/9^{-13}$ with only positive exponents.

Answer 6

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

To simplify the expression 14^(-7)/9^(-13) and rewrite it with positive exponents using the Property of Negative Integer Exponents, we can reciprocate the base and change the sign of the exponent. Here's the step-by-step process:

1. Reciprocate the base and change the sign of the exponent for both terms:
14^(-7) becomes 1/(14^7)
9^(-13) becomes 1/(9^13)

2. Rewrite the expression with positive exponents:
(1/(14^7))/(1/(9^13))

3. To divide by a fraction, we multiply the numerator by the reciprocal of the denominator:
(1/(14^7)) * (9^13/1)

4. Simplify by multiplying the numerators and denominators:
(9^13) / (14^7)

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

Answer 7

[AI-generated answer — Explain Bot]

To find an equivalent expression with only positive exponents, we can use the Property of Negative Integer Exponents, which states that any term raised to a negative exponent can be moved to the denominator and become positive.

The expression given is 14^(-7) / 9^(-13).

Step 1: Move the negative exponents to the denominator and change the signs to positive.

This gives us: 1 / (14^7 * 9^13).

Step 2: Since we want to find an equivalent expression, we can simplify further by evaluating the exponents.

14^7 equals 14 * 14 * 14 * 14 * 14 * 14 * 14, which is a product of seven 14s.

Similarly, 9^13 equals 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9, which is a product of thirteen 9s.

Step 3: Substitute the values of 14^7 and 9^13 back into the expression.

This gives us: 1 / (14 * 14 * 14 * 14 * 14 * 14 * 14 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9).

To simplify this expression further, we could try to find common factors between the terms in the numerator and denominator, but since the expression is already in its simplest form, we cannot simplify it any further.

Therefore, the equivalent expression with only positive exponents is 1 / (14 * 14 * 14 * 14 * 14 * 14 * 14 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9).