Pregunta
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( 4^{\frac{1}{2}} = 2 \) is correct because the square root of 4 is 2.
Solución
Yes, the equation \( 4^{\frac{1}{2}} = 2 \) is **correct**. Here's why:
### Understanding Exponents with Fractions
When you raise a number to a fractional exponent, the denominator of the fraction indicates the root, and the numerator indicates the power. Specifically:
\[
a^{\frac{m}{n}} = \sqrt[n]{a^m} = \left( \sqrt[n]{a} \right)^m
\]
### Applying to \( 4^{\frac{1}{2}} \)
Let's break down \( 4^{\frac{1}{2}} \):
1. **Identify the Root and Power:**
- The exponent \(\frac{1}{2}\) means we're taking the square root of 4.
2. **Calculate the Square Root:**
\[
\sqrt{4} = 2
\]
3. **Therefore:**
\[
4^{\frac{1}{2}} = 2
\]
### Conclusion
Raising 4 to the power of \(\frac{1}{2}\) is equivalent to finding the square root of 4, which is 2. Hence, the equation \( 4^{\frac{1}{2}} = 2 \) holds true.
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución Extra Insights
Did you know that the notation \(4^{\frac{1}{2}}\) is just another way of saying "the square root of 4"? In mathematical terms, \(x^{\frac{1}{n}}\) indicates the n-th root of x. So, when you see that, you might want to think of it as asking what number times itself gives you 4—bingo, it’s 2! In real-world applications, understanding exponents and roots helps in situations like measuring area. For example, if you have a square with an area of 4 square units, finding the side length (using \(4^{\frac{1}{2}}\)) tells you that each side is 2 units long. This knowledge is essential in architecture, landscaping, and many fields where space matters.
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
