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Chapter 5: Problem 5

Multiply each expression using the product rule. $$x^{2} \cdot x^{6} \cdot x^{3}$$

Short Answer

Expert verified
The solution to the given expression is \(x^{11}\).

Step by step solution

01

Identify the Bases and Exponents

In this problem, we are provided with three expressions, \(x^{2}\), \(x^{6}\), and \(x^{3}\). In each of these expressions, the base is 'x' and the exponents are 2, 6, and 3 respectively.
02

Apply the Product Rule of Exponents

According to the product rule of exponents, when multiplying expressions with the same base, the exponents are added. So, we add the exponents 2, 6, and 3 together to get \(x^{2+6+3}\) .
03

Simplify the Expression

Simplify the expression by adding the exponents. The sum of 2, 6, and 3 is 11. So, the solution to the expression \(x^{2+6+3}\) is \(x^{11}\) .

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