Question

question
simplify:
$left(-5z^{4}
ight)^{2}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, for \((-5z^4)^2\), we can apply this rule as follows:
\((-5z^4)^2 = (-5)^2 \cdot (z^4)^2\)

Step2: Simplify each term

First, simplify \((-5)^2\). Squaring a negative number gives a positive result, so \((-5)^2 = 25\).

Next, simplify \((z^4)^2\). Using the power of a power rule \((a^m)^n = a^{m \cdot n}\), we have \((z^4)^2 = z^{4 \cdot 2} = z^8\).

Step3: Multiply the simplified terms

Now, multiply the two simplified terms together: \(25 \cdot z^8 = 25z^8\)

Answer:

\(25z^8\)