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

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 2

are you sure

Answer 3

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 4

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 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.