Question

simplify.
$\left(-5yx^{3}\
ight)^{3}$
write your answer without parentheses.

Explanation:

Step1: Apply power of a product rule

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

Step2: Calculate each part

First, calculate \((-5)^3\). \((-5)^3 = -5 \times -5 \times -5 = -125\). Then, for \((x^3)^3\), we use the power of a power rule \((a^m)^n = a^{mn}\), so \((x^3)^3 = x^{3\times3} = x^9\). And \(y^3\) remains as it is.

Step3: Combine the results

Multiply the results together: \(-125 \times y^3 \times x^9 = -125x^9y^3\).

Answer:

\(-125x^{9}y^{3}\)