/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 Multiply and simplify. $$ \l... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 29

Multiply and simplify. $$ \left(-6 a^{5} b\right)\left(\frac{1}{3} a^{2} b^{2}\right) $$

Short Answer

Expert verified
-2a^{7}b^{3}

Step by step solution

01

Multiply the coefficients

First, multiply the numerical coefficients \(-6\) and \(\frac{1}{3}\): \(-6 \times \frac{1}{3} = -2\).
02

Multiply the powers of a

Next, multiply the variables with the same base. For \(a\), add the exponents: \(a^{5} \times a^{2} = a^{5+2} = a^{7}\).
03

Multiply the powers of b

For \(b\), add the exponents: \(b \times b^{2} = b^{1} \times b^{2} = b^{1+2} = b^{3}\).
04

Combine all parts

Multiply the results from the previous steps: \(-2 \times a^{7} \times b^{3}\). Thus, the simplified expression is \(-2a^{7}b^{3}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Laws of Exponents
To simplify expressions involving exponents, it's crucial to understand the rules governing how exponents work. When you multiply powers with the same base, you add their exponents together. This is due to the rule \(a^m \cdot a^n = a^{m+n}\). Notice how we combine the powers of \(a\) and \(b\) in our exercise: \[ \left( a^5 \cdot a^2 \right) = a^{5+2}= a^7 \] This can be visualized as multiplying several copies of the base: Five \(a\)'s multiplied by two \(a\)'s makes seven \(a\)'s in total.

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Most popular questions from this chapter

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