Question
Use the power rules for exponents to simplify the expression. Give your answer in exponential form. (1/4)^9
Answers
GPT-4o mini
To simplify the expression \((1/4)^9\) using the power rules for exponents, we can write it as:
\[
(1/4)^9 = (4^{-1})^9
\]
Now, applying the power of a power rule, which states \((a^m)^n = a^{m \cdot n}\), we get:
\[
(4^{-1})^9 = 4^{-1 \cdot 9} = 4^{-9}
\]
Thus, the simplified expression in exponential form is:
\[
\boxed{4^{-9}}
\]
\[
(1/4)^9 = (4^{-1})^9
\]
Now, applying the power of a power rule, which states \((a^m)^n = a^{m \cdot n}\), we get:
\[
(4^{-1})^9 = 4^{-1 \cdot 9} = 4^{-9}
\]
Thus, the simplified expression in exponential form is:
\[
\boxed{4^{-9}}
\]