Questions: Use the product rule for exponents to simplify the expression, if possible. (-5 x^3)(-4 x^7)(-3 x) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (-5 x^3)(-4 x^7)(-3 x) = (Type exponential notation with positive exponents. Simplify your answer.) B. The product rule does not apply.

Use the product rule for exponents to simplify the expression, if possible.

(-5 x^3)(-4 x^7)(-3 x)

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. (-5 x^3)(-4 x^7)(-3 x) =
(Type exponential notation with positive exponents. Simplify your answer.)
B. The product rule does not apply.

Transcript text: possible Use the product rule for exponents to simplify the expression, if possible. \[ \left(-5 x^{3}\right)\left(-4 x^{7}\right)(-3 x) \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\left(-5 x^{3}\right)\left(-4 x^{7}\right)(-3 x)=$ $\square$ (Type exponential notation with positive exponents. Simplify your answer.) B. The product rule does not apply. (1) Time Remaining: 01:40:18 Next

Solution

Solution Steps

To simplify the expression using the product rule for exponents, we need to multiply the coefficients and add the exponents of like bases. The expression $(-5 x^{3})(-4 x^{7})(-3 x)$ involves multiplying the coefficients $-5$, $-4$, and $-3$, and adding the exponents of $x$ which are $3$, $7$, and $1$.

Step 1: Multiply the Coefficients

We start with the expression $(-5 x^{3})(-4 x^{7})(-3 x)$. First, we multiply the coefficients: \[ -5 \times -4 \times -3 = -60 \]

Step 2: Add the Exponents

Next, we add the exponents of $x$: \[ 3 + 7 + 1 = 11 \]

Step 3: Combine the Results

Now, we combine the results from the previous steps to form the simplified expression: \[ (-5 x^{3})(-4 x^{7})(-3 x) = -60 x^{11} \]