Asked by NIGAS
which of the following is equivalent expression to 14^-7/9^-13 with only positive exponents generated by applying the properties of negative integer exponents?
Answers
Answered by
NIGAS
what?
Answered by
GPT 3.5
To simplify the expression with positive exponents, we can apply the property that states: \(a^{-m} = \frac{1}{a^m}\).
Starting with the expression \(14^{-7}/9^{-13}\), let's apply this property to each term:
\(\frac{1}{14^7} \cdot \frac{1}{9^{13}}\).
Now, let's apply another property: \(a^{m} \cdot a^{n} = a^{m+n}\).
\(\frac{1}{14^7} \cdot \frac{1}{9^{13}} = \frac{1}{14^7 \cdot 9^{13}}\).
Thus, the equivalent expression with only positive exponents is \(\frac{1}{14^7 \cdot 9^{13}}\).
Starting with the expression \(14^{-7}/9^{-13}\), let's apply this property to each term:
\(\frac{1}{14^7} \cdot \frac{1}{9^{13}}\).
Now, let's apply another property: \(a^{m} \cdot a^{n} = a^{m+n}\).
\(\frac{1}{14^7} \cdot \frac{1}{9^{13}} = \frac{1}{14^7 \cdot 9^{13}}\).
Thus, the equivalent expression with only positive exponents is \(\frac{1}{14^7 \cdot 9^{13}}\).
Answered by
GPT 3.5
Apologies for the confusion. Let's approach the problem again.
To simplify the expression \(14^{-7}/9^{-13}\) using only positive exponents, we can apply the rule that \(a^{-m} = \frac{1}{a^m}\).
Applying this rule to the expression, we get:
\(\frac{1}{14^7}/\frac{1}{9^{13}}\).
Next, we can use the rule that \(a/b = \frac{a}{1} \cdot \frac{1}{b}\).
So, we have:
\(\frac{1}{14^7} \cdot \frac{9^{13}}{1}\).
Finally, we can simplify further by using the rule that \(a^m \cdot b^m = (a \cdot b)^m\).
Thus, we get:
\(\frac{9^{13}}{14^7}\).
Therefore, the equivalent expression with positive exponents is \(\frac{9^{13}}{14^7}\).
To simplify the expression \(14^{-7}/9^{-13}\) using only positive exponents, we can apply the rule that \(a^{-m} = \frac{1}{a^m}\).
Applying this rule to the expression, we get:
\(\frac{1}{14^7}/\frac{1}{9^{13}}\).
Next, we can use the rule that \(a/b = \frac{a}{1} \cdot \frac{1}{b}\).
So, we have:
\(\frac{1}{14^7} \cdot \frac{9^{13}}{1}\).
Finally, we can simplify further by using the rule that \(a^m \cdot b^m = (a \cdot b)^m\).
Thus, we get:
\(\frac{9^{13}}{14^7}\).
Therefore, the equivalent expression with positive exponents is \(\frac{9^{13}}{14^7}\).