Let's break down the given expression step-by-step. We need to simplify and evaluate [tex]\( 9^{\frac{1}{5}} \times \left(3^{\frac{3}{10}}\right)^2 \)[/tex].
1. Evaluate [tex]\( 9^{\frac{1}{5}} \)[/tex]:
The term [tex]\( 9^{\frac{1}{5}} \)[/tex] represents the fifth root of 9. Numerically, this evaluates to approximately [tex]\( 1.5518455739153598 \)[/tex].
2. Evaluate [tex]\( \left(3^{\frac{3}{10}}\right)^2 \)[/tex]:
First, simplify the inner exponentiation [tex]\( 3^{\frac{3}{10}} \)[/tex]. Then we take the square of this result.
- Evaluate [tex]\( 3^{\frac{3}{10}} \)[/tex]:
Numerically, this is approximately [tex]\( 1.3903891703159094 \)[/tex].
- Now square this result:
[tex]\( (1.3903891703159094)^2 \approx 1.9331820449317625 \)[/tex].
3. Multiply the results:
Now, multiply the results of the two parts we have calculated:
[tex]\[ 9^{\frac{1}{5}} \times \left(3^{\frac{3}{10}}\right)^2 = 1.5518455739153598 \times 1.9331820449317625 \][/tex]
The product of these two values is approximately:
[tex]\[ 3.0 \][/tex]
Thus, the expression [tex]\( 9^{\frac{1}{5}} \times \left(3^{\frac{3}{10}}\right)^2 \)[/tex] simplifies to approximately [tex]\( 3.0 \)[/tex].
