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Chapter 7: Problem 85

Simplify: \(\left(3 x^{2}\right)\left(-4 x^{-10}\right) .\) (Section 5.7, Example 3)

Short Answer

Expert verified
\(-12 x^{-8}\) or \(-12/x^{8}\)

Step by step solution

01

Recognize the rule

It is important to know that when multiplying two powers with the same base, the exponents can be added. The multiplication rule is \(a^{m} \cdot a^{n} = a^{m+n}\). Also, a negative exponent means to take the reciprocal of the base to that positive exponent.
02

Apply the multiplication rule

Applying the multiplication rule, we get: \(\left(3 x^{2}\right)\left(-4 x^{-10}\right) = 3*(-4) \cdot x^{(2+(-10))}\).
03

Simplify the expression

Simplify to get the final expression: \(-12 x^{-8}\). Remember that this means -12 divided by \(x^{8}\) or \(-12/x^{8}\).

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{4}{x}+\frac{3}{x-5}$$

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