?(1 point)
5 answers
To rewrite \( \sqrt[4]{23} \) in exponential form, we can express it using rational exponents.
The fourth root of \( 23 \) can be expressed as:
\[ \sqrt[4]{23} = 23^{1/4} \]
So the rational number that could be used as an exponent to rewrite \( \sqrt[4]{23} \) is \( \frac{1}{4} \).
To rewrite \( 9^{1/3} \) using a root, we can express it as a cube root.
The expression \( 9^{1/3} \) can be rewritten as:
\[ \sqrt[3]{9} \]
So, \( 9^{1/3} \) is equal to \( \sqrt[3]{9} \).
To simplify \( 27^{1/3} \), we can find the cube root of \( 27 \).
Since \( 27 = 3^3 \), we have:
\[ 27^{1/3} = (3^3)^{1/3} \]
Using the property of exponents \((a^m)^n = a^{m \cdot n}\):
\[ (3^3)^{1/3} = 3^{3 \cdot \frac{1}{3}} = 3^1 = 3 \]
Therefore, the simplified form of \( 27^{1/3} \) is \( 3 \).
