/*! 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 125 Why is \(\left(-3 x^{2}\right)\l... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 125

Why is \(\left(-3 x^{2}\right)\left(2 x^{-5}\right)\) not simplified? What must be done to simplify the expression?

Short Answer

Expert verified
The expression \(\left(-3 x^{2}\right)\left(2 x^{-5}\right)\) is not simplified originally because it involves two monomials with the same bases but different exponents that can be combined by applying the multiplication rule of exponents. After simplifying, it becomes \(-6x^{-3}\).

Step by step solution

01

Identify the parts of the expression

The original expression is a product of two monomials: \(-3x^2\) and \(2x^{-5}\). Each monomial consists of number part called the coefficient and the variable part, here being \(x^2\) and \(x^{-5}\) respectively.
02

Apply the multiplication rule of exponents

The multiplication rule of exponents states that when multiplying two powers with the same bases, one should add the exponents. Here, both terms have base x. So multiplying them together, we have: \((-3x^2) * (2x^{-5}) = -6x^{2 + (-5)}\)
03

Simplify the expression

Now, simplifying the power of x: \(x^{2 + (-5)}\) becomes \(x^{-3}\). Thus, the simplified version of the given expression is \(-6x^{-3}\).

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