Problem 127 Why is \(\left(-3 x^{2}\right)\l... [FREE SOLUTION]

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College Algebra

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 0: Problem 127

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

So, the simplified form of the given expression $\left(-3 x^{2}\right)\left(2 x^{-5}\right)$ is $-6x^{-3}$.

Step by step solution

Recognize the Constants and Exponents

In this expression, you have two parts: $-3x^2$ and $2x^{-5}$. In both parts you can see a constant and an $x$ term with an exponent. The first part has the constant $-3$ and the $x$ term $x^2$. The second part has the constant $2$ and the $x$ term $x^{-5}$.

Multiply the Constants

You first multiply the constants -3 and 2. The multiplication of -3 and 2 gives -6. So, the simplified form of the constants will be -6.

Multiply x terms

According to the exponent rule when you multiply terms with the same base, you add the exponents. Given $x^2$ and $x^{-5}$, the base is $x$ and the exponents that need to be added are 2 and -5. Adding 2 and -5 gives -3. So, the simplified form of the $x$ terms is $x^{-3}$.

Combine Simplified Constants and x terms

Combine the simplified constants and $x$ terms from steps 2 and 3 to get your final simplified expression. Multiplying the constants -6 with the $x$ term $x^{-3}$ gives $-6x^{-3}$.

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91影视

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

Short Answer

Step by step solution

Recognize the Constants and Exponents

Multiply the Constants

Multiply x terms

Combine Simplified Constants and x terms

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