Question

1. the expression $(-6c^{4}d^{3})^{3}$ is equivalent to

(1) $-216c^{7}d^{6}$
(3) $216c^{7}d^{6}$
(2) $-216c^{12}d^{9}$
(4) $-216c$

Explanation:

Step1: Apply power of a product rule

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

Step2: Calculate each part

• Calculate \((-6)^3\): \((-6)^3 = -6 \times -6 \times -6 = -216\)
• Calculate \((c^4)^3\) using the power of a power rule \((a^m)^n = a^{m \times n}\): \((c^4)^3 = c^{4 \times 3} = c^{12}\)
• Calculate \((d^3)^3\) using the power of a power rule: \((d^3)^3 = d^{3 \times 3} = d^9\)

Step3: Combine the results

Multiply the results from Step 2 together:
\((-6)^3 \cdot (c^4)^3 \cdot (d^3)^3 = -216 \cdot c^{12} \cdot d^9 = -216c^{12}d^9\)

Answer:

(2) -216c¹²d⁹