Which of the following is an equivalent Expression 214 with a negative power of 7/9 with a negative power of 13 which only positive exponents generated by applying the property of negative integer exponents with the answer be over nine with the power of 13 and -14 with a negative power of seven or would the answer be nine with the power of 13/14 with a power of seven or 14 with a negative power of 7×9 with the power of 13 or would it be 14 power of seven or nine with the power of 13

Answer 1

To understand the equivalent expression you are looking for, let's clarify the properties of negative exponents.

The property states that for any non-zero number \( a \) and any integer \( n \): \[ a^{-n} = \frac{1}{a^n} \]

Let's rephrase the question to identify potential expressions that result from a power of \( \frac{7}{9} \) with negative powers of \( 13 \) and \( 7 \).

1. If we have \( \left( \frac{7}{9} \right)^{-n} \), it transforms as follows: \[ \left( \frac{7}{9} \right)^{-n} = \frac{9^n}{7^n} \]

Let's now consider the forms you provided and translate them into mathematical expressions with positive exponents when possible:

1. Expression: \(\frac{9^{13}}{7^{14}}\) (This has positive exponents).
2. Expression: \(\frac{9^{\frac{13}{14}}}{7}\) (This is also valid).
3. Expression: \(14 \cdot 7^{-1} \cdot 9^{13}\) (This has a negative exponent applied to 7).
4. Expression: \(14 \cdot 7^1\) (This is valid but lacks a reference to 9).

Considering the options and applying the rule of negative exponents, it’s necessary for the answer to have only positive exponents:

Assuming we rewrite whatever expression you are asking about for clarity:

• If you start with something like \( \left( \frac{13}{9} \right)^{-n} \) or any fraction thereof, your result should remain in a form that respects positive exponents.

So, from your options:

• Expression with \( 9^{13} \) and \( 7^{14} \) with positive exponents would best represent a form consistent with the rules of negative exponents.

Without precise definitions of your expressions, I would conclude that the equivalent expression that preserves positive exponents would likely be:

\(\frac{9^{13}}{7^{14}}\)

Please verify and clarify any specific details of your expressions, and we might draw more accurate deductions.