Let’s carefully evaluate the expression [tex]\((3y + x)^{\frac{3}{2}}\)[/tex]. Break down the calculation into detailed steps:
1. Identify the Expression:
The given expression is [tex]\((3y + x)^{\frac{3}{2}}\)[/tex].
2. Exponent Interpretation:
The exponent [tex]\(\frac{3}{2}\)[/tex] can be interpreted in two ways:
[tex]\[
\left(3y + x\right)^{\frac{3}{2}} = (\left(3y + x\right)^{1.5})
\][/tex]
This can be further broken down as:
[tex]\[
(\left(3y + x\right)^{1.5}) = (\left(3y + x\right)^1 \cdot (\left(3y + x\right)^{0.5}))^3
\][/tex]
However, it's more common to simply treat [tex]\(\frac{3}{2}\)[/tex] as 1.5 for simplicity.
3. Final Expression:
Therefore, the simplified form of the expression remains:
[tex]\[
\boxed{(3y + x)^{1.5}}
\][/tex]
This expression reveals the same relationship as initially defined, evaluated to [tex]\((3y + x)^{1.5}\)[/tex].
