Find each product. Assume all variables represent positive real numbers. y^5/8(y^3/8-10y^11/8)

Verified step by step guidance

1. Distribute \( y^{5/8} \) to each term inside the parentheses.
2. Multiply \( y^{5/8} \) by \( y^{3/8} \).
3. Use the property of exponents: \( a^m \cdot a^n = a^{m+n} \).
4. Multiply \( y^{5/8} \) by \(-10y^{11/8} \).
5. Use the property of exponents again: \( a^m \cdot a^n = a^{m+n} \) and simplify the expression.

Key Concepts

Exponents and Powers

Exponents represent repeated multiplication of a base number. In the expression y^(5/8), the exponent 5/8 indicates that y is multiplied by itself 5/8 times, which can be interpreted as the eighth root of y raised to the fifth power. Understanding how to manipulate exponents is crucial for simplifying expressions and performing operations like multiplication and division.

Factoring Expressions

Factoring involves rewriting an expression as a product of its factors. In the given expression, y^(5/8) can be factored out from both terms in the parentheses, y^(3/8) and -10y^(11/8). This process simplifies the expression and makes it easier to work with, especially when solving equations or finding products.

Polynomial Operations

Polynomial operations include addition, subtraction, multiplication, and division of polynomial expressions. In this case, the expression involves multiplying a monomial (y^(5/8)) by a polynomial (y^(3/8) - 10y^(11/8)). Understanding how to perform these operations is essential for simplifying and solving algebraic expressions effectively.