Sure! Here is how you can rewrite [tex]\( 9^{\frac{1}{3}} \)[/tex] using a root:
1. Understand the Exponent: The expression [tex]\( 9^{\frac{1}{3}} \)[/tex] indicates taking the cube root of 9. When the exponent is a fraction [tex]\( \frac{1}{n} \)[/tex], it corresponds to the [tex]\( n \)[/tex]th root of the base number. In this case, [tex]\( \frac{1}{3} \)[/tex] tells us we are looking for the cube root.
2. Rewrite Using Root Notation: The expression [tex]\( 9^{\frac{1}{3}} \)[/tex] can be rewritten using the root symbol (∛). Specifically, the cube root of 9 can be written as:
[tex]\[
9^{\frac{1}{3}} = \sqrt[3]{9}
\][/tex]
So, [tex]\( 9^{\frac{1}{3}} \)[/tex] can be expressed as [tex]\( \sqrt[3]{9} \)[/tex], which can also be denoted using the cube root symbol [tex]\( ∛9 \)[/tex].
Thus, the answer is:
[tex]\[
∛9
\][/tex]
