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 \(\frac{1}{14^7 \cdot 9^{13}}\).
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?
3 answers
what?
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 \(\frac{9^{13}}{14^7}\).