To rewrite the expression [tex]\(9x^{\frac{3}{2}}\)[/tex] as a radical expression, we need to follow these steps:
1. Understand the Rational Exponent:
The exponent [tex]\(\frac{3}{2}\)[/tex] can be interpreted in terms of radicals.
- The denominator of the fraction (2) indicates a square root.
- The numerator (3) indicates that the base [tex]\(x\)[/tex] is raised to the power of 3.
2. Rewrite the Expression:
We rewrite [tex]\(x^{\frac{3}{2}}\)[/tex] using radical notation. The expression inside the exponent can be broken down as follows:
[tex]\[
x^{\frac{3}{2}} = (x^3)^\frac{1}{2} = \sqrt{x^3}
\][/tex]
3. Combine with the Coefficient:
Now, we need to reattach the coefficient 9, which was originally multiplied by [tex]\(x^{\frac{3}{2}}\)[/tex].
Therefore, the full expression [tex]\(9x^{\frac{3}{2}}\)[/tex] in radical form is:
[tex]\[
9 \cdot \sqrt{x^3}
\][/tex]
So, rewriting [tex]\(9x^{\frac{3}{2}}\)[/tex] as a radical expression gives us:
[tex]\[
9 \sqrt{x^3}
\][/tex]
This correctly transforms the expression with a rational exponent into its equivalent radical form.
