Question

use the power rule and the power of a product rule to simplify the expression.
$(3z^3)^2$
$(3z^3)^2 = \square$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((3z^3)^2\), we can apply this rule to get \(3^2 \cdot (z^3)^2\).

Step2: Apply power rule to exponents

The power rule states that \((a^m)^n = a^{m \cdot n}\). For \((z^3)^2\), we have \(z^{3 \cdot 2}=z^6\). And \(3^2 = 9\).

Step3: Multiply the results

Multiply the results from Step 1 and Step 2: \(9 \cdot z^6 = 9z^6\).

Answer:

\(9z^6\)