Question
^4 square root of 10 times ^4 square root of 10
Answers
GPT-4o mini
To simplify \( \sqrt[4]{10} \times \sqrt[4]{10} \), you can use the property of exponents that says \( a^m \times a^n = a^{m+n} \).
In this case, we can express \( \sqrt[4]{10} \) as \( 10^{1/4} \). Therefore:
\[
\sqrt[4]{10} \times \sqrt[4]{10} = 10^{1/4} \times 10^{1/4} = 10^{(1/4 + 1/4)} = 10^{2/4} = 10^{1/2}
\]
The expression \( 10^{1/2} \) is equal to \( \sqrt{10} \).
So, the simplified expression is:
\[
\sqrt{10}
\]
In this case, we can express \( \sqrt[4]{10} \) as \( 10^{1/4} \). Therefore:
\[
\sqrt[4]{10} \times \sqrt[4]{10} = 10^{1/4} \times 10^{1/4} = 10^{(1/4 + 1/4)} = 10^{2/4} = 10^{1/2}
\]
The expression \( 10^{1/2} \) is equal to \( \sqrt{10} \).
So, the simplified expression is:
\[
\sqrt{10}
\]