(2x+3y)^(3/2)
you want it using the binomial expansion? You can't reduce it much as-is.
To simplify the expression (2x + 3y)^(3/2), you can follow these steps:
Step 1: Recognize that (2x + 3y) is a binomial, which means it has two terms: 2x and 3y.
Step 2: Apply the exponent 3/2 to each term separately.
For the term 2x:
(2x)^(3/2)
For the term 3y:
(3y)^(3/2)
Step 3: To simplify each term raised to the exponent 3/2, you can rewrite it as the square root of the term raised to the power of 3:
(2x)^(3/2) = √((2x)^3)
(3y)^(3/2) = √((3y)^3)
Step 4: Simplify the expressions within the square roots by applying the power rule of exponents:
(2x)^(3/2) = √(2^3 * x^3)
= √(8x^3)
= √8 * √x^3
= 2√2 * x√x
(3y)^(3/2) = √(3^3 * y^3)
= √(27y^3)
= √27 * √y^3
= 3√3 * y√y
So, the simplified expression is:
2√2 * x√x + 3√3 * y√y