Find each product. Assume all variables represent positive real numbers. −4k(k7/3−6k1/3)-4k \left( $$k^{7/3}$$ - $$6k^{1/3}$$ \right) −4k(k7/3−6k1/3)

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 73

1장, 문제 73

Find each product. Assume all variables represent positive real numbers. $-4k $\left$( k^{7/3} - 6k^{1/3} $\right$)$

검증된 단계별 안내

Start by distributing the term outside the parentheses, which is $-4k$, to each term inside the parentheses: $-4k \times k^{7/3}$ and $-4k \times (-6k^{1/3})$.

Recall the property of exponents when multiplying like bases: $a^m \times a^n = a^{m+n}$. Use this to combine the powers of $k$ in each product.

For the first product, add the exponents of $k$: $1$ (from $k$) plus $\frac{7}{3}$ (from $k^{7/3}$), so the exponent becomes $1 + \frac{7}{3}$.

For the second product, multiply the constants $-4$ and $-6$ to get a positive product, then add the exponents of $k$: $1$ (from $k$) plus $\frac{1}{3}$ (from $k^{1/3}$), so the exponent becomes $1 + \frac{1}{3}$.

Write the final expression as the sum of the two terms with their simplified coefficients and exponents, using the results from the previous steps.

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주요 개념

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

Properties of Exponents

Understanding how to manipulate exponents is essential, including the product rule which states that when multiplying like bases, you add their exponents. For example, k^a * k^b = k^(a+b). This helps simplify expressions involving variables raised to fractional powers.

Distributive Property

The distributive property allows you to multiply a single term across terms inside parentheses. For instance, a(b + c) = ab + ac. Applying this property correctly is crucial to expanding and simplifying algebraic expressions.

Fractional Exponents

Fractional exponents represent roots, such as k^(1/3) meaning the cube root of k. Recognizing and working with fractional exponents helps in simplifying expressions and combining like terms when variables have fractional powers.

Find each product. Assume all variables represent positive real numbers. −4k(k7/3−6k1/3)-4k \(\left\)( k^{7/3} - 6k^{1/3} \(\right\)) −4k(k7/3−6k1/3)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Properties of Exponents

Distributive Property

Fractional Exponents

Find each product. Assume all variables represent positive real numbers. $-4k \(\left\)( k^{7/3} - 6k^{1/3} \(\right\))$