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Chapter 0: Problem 45

Simplify each exponential expression. $$\left(3 x^{4}\right)\left(2 x^{7}\right)$$

Short Answer

Expert verified
The simplified form of the given exponential expression is \(6x^{11}\).

Step by step solution

01

Identify the base and the exponents

Here, the base is \(x\), while the exponents are 4 and 7. The coefficients are 3 and 2 respectively.
02

Multiply the coefficients

Firstly, multiply the coefficients 3 and 2 together, which equals 6.
03

Apply the law of exponents

According to the law of exponents for multiplication, \(a^n \cdot a^m = a^{n+m}\), where \(a\) is the base and \(n\) and \(m\) are the exponents, apply this rule to the exponents 4 and 7. This yields \(x^{4+7} = x^{11}\).
04

Combine the results

Combine the result from steps 2 and 3 to get the simplified expression, which is \(6x^{11}\).

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