Respuesta :
Given that the expression in the question is [tex]\displaystyle x^{\frac{5}{2} }[/tex], the equivalent expression
can be found using the rules of indices.
- [tex]\displaystyle \underline{x^{\frac{5}{2} } \ is \ equivalent \ to \ x^2 \cdot\sqrt{x}}[/tex]
Reasons:
The given expression is [tex]\displaystyle x^{\frac{5}{2} }[/tex]
Required:
To find the equivalent expression
Solution:
According to the rules of indices, we have;
[tex]a^{n + m} = a^n \times a^m[/tex]
[tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
Therefore, the above expression can be expanded as follows;
[tex]\displaystyle x^{\frac{5}{2} } = x ^{2.5} = \mathbf{x^{2 + 0.5}}[/tex]
[tex]\displaystyle x^{2 + 0.5} =\mathbf{ x^2 \times x^{0.5}}[/tex]
Which gives;
[tex]\displaystyle x^2 \times x^{0.5} = \mathbf{x^2 \times \sqrt{x}}[/tex]
Therefore;
[tex]\displaystyle x^{\frac{5}{2} } \equiv x^2 \cdot\sqrt{x}[/tex], which is the form [tex]a^{\frac{n}{m} } = \sqrt[m]{a^n}[/tex]
[tex]\underline{An \ expression \ \mathbf{equivalent} \ to \ x^\frac{5}{2} \ is \ x^2 \cdot \sqrt{x}}[/tex]
Learn more about the rules of indices here:
https://brainly.com/question/8959311
