Question

simplify the expression below.
$(-4x^{6})^{3}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((-4x^6)^3\), we can apply this rule as follows:
\((-4x^6)^3 = (-4)^3 \cdot (x^6)^3\)

Step2: Calculate \((-4)^3\)

\((-4)^3 = -4 \times -4 \times -4 = -64\)

Step3: Apply power of a power rule

The power of a power rule states that \((a^m)^n = a^{m \times n}\). So for \((x^6)^3\), we have:
\((x^6)^3 = x^{6 \times 3} = x^{18}\)

Step4: Combine the results

Now we combine the results from Step 2 and Step 3:
\((-4)^3 \cdot (x^6)^3 = -64 \cdot x^{18} = -64x^{18}\)

Answer:

\(-64x^{18}\)