Find each product. Assume all variables represent positive real numbers. y5/8(y3/8−$$10y11/8)y^{5/8}$$ \left( $$y^{3/8}$$ - $$10y^{11/8}$$ \right) y5/8(y3/8−10y11/8)

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 71

1장, 문제 71

Find each product. Assume all variables represent positive real numbers. $y^{5/8} $\left$( y^{3/8} - 10y^{11/8} $\right$)$

검증된 단계별 안내

Identify the expression to be simplified: $y^{\frac{5}{8}} \left(y^{\frac{3}{8}} - 10y^{\frac{11}{8}}\right)$.

Apply the distributive property by multiplying $y^{\frac{5}{8}}$ with each term inside the parentheses separately: $y^{\frac{5}{8}} \cdot y^{\frac{3}{8}}$ and $y^{\frac{5}{8}} \cdot (-10y^{\frac{11}{8}})$.

Use the rule of exponents for multiplying powers with the same base: $a^m \cdot a^n = a^{m+n}$. So, add the exponents when multiplying the $y$ terms.

Calculate the exponents for each product: For the first term, add $\frac{5}{8} + \frac{3}{8}$; for the second term, add $\frac{5}{8} + \frac{11}{8}$.

Rewrite the expression with the new exponents and simplify the coefficients: $y^{\text{sum of exponents}}$ for each term, keeping the $-10$ coefficient in the second term.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Laws of Exponents

The laws of exponents govern how to multiply, divide, and simplify expressions with powers. When multiplying terms with the same base, add their exponents. For example, y^(5/8) * y^(3/8) = y^((5/8)+(3/8)) = y^(8/8) = y^1. Understanding these rules is essential for simplifying the given expression.

Distributive Property

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis. In this problem, y^(5/8) must be multiplied by both y^(3/8) and -10y^(11/8), distributing the multiplication across the terms.

Simplifying Algebraic Expressions

Simplifying involves combining like terms and reducing expressions to their simplest form. After applying exponent rules and distribution, combine powers and constants carefully. Since all variables are positive, no absolute values or domain restrictions affect simplification.

Find each product. Assume all variables represent positive real numbers. y5/8(y3/8−10y11/8)y^{5/8} \(\left\)( y^{3/8} - 10y^{11/8} \(\right\)) y5/8(y3/8−10y11/8)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Laws of Exponents

Distributive Property

Simplifying Algebraic Expressions

Find each product. Assume all variables represent positive real numbers. $y^{5/8} \(\left\)( y^{3/8} - 10y^{11/8} \(\right\))$