Answer :
To find the equivalent expression for [tex]\( 4x^{\frac{1}{2}} \)[/tex], we need to understand and manipulate the given expression step by step.
1. Understanding the exponent [tex]\( \frac{1}{2} \)[/tex]:
- The term [tex]\( x^{\frac{1}{2}} \)[/tex] can be interpreted as the square root of [tex]\( x \)[/tex]. This is because, by definition, raising a number to the power of [tex]\( \frac{1}{2} \)[/tex] is the same as taking the square root of that number.
2. Rewriting the expression:
- Substitute the square root interpretation into the expression:
[tex]\[ x^{\frac{1}{2}} = \sqrt{x} \][/tex]
3. Multiplication by 4:
- The given expression is [tex]\( 4x^{\frac{1}{2}} \)[/tex]. By applying the square root substitution, we get:
[tex]\[ 4x^{\frac{1}{2}} = 4 \cdot \sqrt{x} \][/tex]
Thus, the expression [tex]\( 4 x^{\frac{1}{2}} \)[/tex] is equivalent to [tex]\( 4 \cdot \sqrt{x} \)[/tex].
Therefore, the final simplified form of the given expression is:
[tex]\[ 4 \sqrt{x} \][/tex]
1. Understanding the exponent [tex]\( \frac{1}{2} \)[/tex]:
- The term [tex]\( x^{\frac{1}{2}} \)[/tex] can be interpreted as the square root of [tex]\( x \)[/tex]. This is because, by definition, raising a number to the power of [tex]\( \frac{1}{2} \)[/tex] is the same as taking the square root of that number.
2. Rewriting the expression:
- Substitute the square root interpretation into the expression:
[tex]\[ x^{\frac{1}{2}} = \sqrt{x} \][/tex]
3. Multiplication by 4:
- The given expression is [tex]\( 4x^{\frac{1}{2}} \)[/tex]. By applying the square root substitution, we get:
[tex]\[ 4x^{\frac{1}{2}} = 4 \cdot \sqrt{x} \][/tex]
Thus, the expression [tex]\( 4 x^{\frac{1}{2}} \)[/tex] is equivalent to [tex]\( 4 \cdot \sqrt{x} \)[/tex].
Therefore, the final simplified form of the given expression is:
[tex]\[ 4 \sqrt{x} \][/tex]
