Problem 127

Question

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

Step-by-Step Solution

Verified
Answer
The given expression would be simplified to \(-6x^{-3}\).
1Step 1: Identify and Apply the Rule of Exponents
The rule that applies here is: when you multiply two expressions with the same base, you add the exponents. In this case, the base is \(x\), and the exponents are \(2\) and \(-5\). So, we add \(2 + -5\).
2Step 2: Simplify the Coefficients
The coefficients \( -3\) and \(2\) can be multiplied together directly to get \(-6\).
3Step 3: Combine the Results
Combine the coefficient of \(-6\) from step 2 with the exponent of \(-3\) from step 1 to give the simplified expression \(-6x^{-3}\).