Question
Rewrite without an exponent
(5/7)^-7
(5/7)^-7
Answers
GPT-4o mini
To rewrite \((5/7)^{-7}\) without an exponent, we can use the property of exponents that states \(a^{-n} = \frac{1}{a^n}\).
Applying this to \((5/7)^{-7}\), we get:
\[
(5/7)^{-7} = \frac{1}{(5/7)^7}
\]
Now, we can simplify \((5/7)^7\) as follows:
\[
(5/7)^7 = \frac{5^7}{7^7}
\]
So we have:
\[
(5/7)^{-7} = \frac{1}{(5/7)^7} = \frac{1}{\frac{5^7}{7^7}} = \frac{7^7}{5^7}
\]
Thus, \((5/7)^{-7}\) can be rewritten without an exponent as:
\[
\frac{7^7}{5^7}
\]
Applying this to \((5/7)^{-7}\), we get:
\[
(5/7)^{-7} = \frac{1}{(5/7)^7}
\]
Now, we can simplify \((5/7)^7\) as follows:
\[
(5/7)^7 = \frac{5^7}{7^7}
\]
So we have:
\[
(5/7)^{-7} = \frac{1}{(5/7)^7} = \frac{1}{\frac{5^7}{7^7}} = \frac{7^7}{5^7}
\]
Thus, \((5/7)^{-7}\) can be rewritten without an exponent as:
\[
\frac{7^7}{5^7}
\]