use the product rule to simply the expression . write your answer in exponential notation (-5x raise to the power of 8) multiply by (-2x raised to the power of 5)

Answer 1

To simplify the expression (-5x)^8 * (-2x)^5 using the product rule, we need to multiply the base and add the exponents.

The product rule states that (a^m) * (a^n) = a^(m + n).

Applying this rule to the given expression, we have:

(-5x)^8 * (-2x)^5
= (-5)^8 * (x)^8 * (-2)^5 * (x)^5 (using the power of a product rule)
= (-5)^8 * (-2)^5 * (x)^8 * (x)^5 (rearranging the terms)

Now, let's simplify the expression further:

=(-5)^8 * (-2)^5 * x^(8 + 5)
=(-5)^8 * (-2)^5 * x^13

Therefore, the simplified expression in exponential notation is:

(-5x)^8 * (-2x)^5 = (-5)^8 * (-2)^5 * x^13