Question

1. simplify the expression. write your answer using only positive exponents.

$(-2n)^5 = \square$

Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((-2n)^5\), we can apply this rule as follows:
\((-2n)^5 = (-2)^5 \times n^5\)

Step2: Calculate \((-2)^5\)

We know that \((-2)^5 = (-2) \times (-2) \times (-2) \times (-2) \times (-2)\). Let's calculate this:
\((-2) \times (-2) = 4\), \(4 \times (-2) = -8\), \(-8 \times (-2) = 16\), \(16 \times (-2) = -32\)
So \((-2)^5 = -32\) and \(n^5\) remains as it is (since we already have a positive exponent for \(n\)).

Step3: Combine the results

Putting it together, we have \((-2n)^5 = -32n^5\)

Answer:

\(-32n^5\)