f(x) = ³√x ( 2x² + ⁵√x )

To solve the given equation, we need to simplify the expression first. Let's break it down step by step:

Step 1: Simplify the expression inside the parentheses.

• The expression inside the parentheses is 2x² + ⁵√x.
• There is no way to simplify this expression further, so we leave it as it is.

Step 2: Simplify the expression outside the parentheses.

• The expression outside the parentheses is ³√x.
• This can be rewritten as x^(1/3), using exponent notation.

Step 3: Multiply the expressions inside and outside the parentheses.

• Multiplying x^(1/3) with 2x² + ⁵√x gives us x^(1/3) * (2x² + ⁵√x).

Step 4: Distribute the exponent x^(1/3) to each term inside the parentheses.

• Distributing the exponent gives us (x^(1/3) * 2x²) + (x^(1/3) * ⁵√x).

Step 5: Simplify each term separately.

• Simplifying the first term, x^(1/3) * 2x², we can combine the exponents by adding them: x^(1/3 + 2) = x^(7/3).
• Simplifying the second term, x^(1/3) * ⁵√x, we can combine the exponents by multiplying them: x^(1/3 * 1/5) = x^(1/15).

Step 6: Combine the simplified terms.

• Combining the simplified terms, we have x^(7/3) + x^(1/15).

So, the simplified expression for f(x) is x^(7/3) + x^(1/15).