Question

simplify.
$(-5a^{4}b)^{3}$
write your answer without parentheses.

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((xy)^n = x^n y^n\). So for \((-5a^4b)^3\), we can apply this rule to each factor inside the parentheses: \((-5)^3 \cdot (a^4)^3 \cdot b^3\).

Step2: Calculate each term

• Calculate \((-5)^3\): \((-5)^3 = -5 \times -5 \times -5 = -125\).
• Calculate \((a^4)^3\) using the power of a power rule \((x^m)^n = x^{m \times n}\): \((a^4)^3 = a^{4 \times 3} = a^{12}\).
• \(b^3\) remains as it is.

Step3: Multiply the results together

Multiply the three results: \(-125 \cdot a^{12} \cdot b^3 = -125a^{12}b^3\).

Answer:

\(-125a^{12}b^3\)