Problem 85 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: Apply the multiplication rule

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

Step 3: Simplify the expression

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