To rewrite the expression \(4^{\frac{2}{5} \cdot \frac{1}{4}}\) with a rational exponent as a radical expression, we first simplify the exponent:
\[ \frac{2}{5} \cdot \frac{1}{4} = \frac{2 \cdot 1}{5 \cdot 4} = \frac{2}{20} = \frac{1}{10} \]
Thus, the expression simplifies to:
\[ 4^{\frac{1}{10}} \]
This can be expressed as a radical:
\[ \sqrt[10]{4} \]
Now, let's evaluate the options given:
a) the tenth root of four → \( \sqrt[10]{4} \)
b) the fourth root of four → \( \sqrt[4]{4} \)
c) the fifth root of four squared → \( \sqrt[5]{4^2} \)
d) the square root of four to the tenth power → \( \sqrt{4^{10}} \)
The correct answer is: a) the tenth root of four.
1 answer