Question

question 5
1 pts
an expression is given below.
(2x^{3}y)^{3}
choose an equivalent expression.
8x^{9}y^{3}
8x^{9}y^{6}
6x^{9}y^{3}
6x^{9}y^{6}

Explanation:

Step1: Apply power - of - a - product rule

According to the rule \((ab)^n=a^n b^n\), for \((2x^{2}y)^{3}\), we have \((2x^{2}y)^{3}=2^{3}(x^{2})^{3}y^{3}\).

Step2: Calculate \(2^{3}\) and apply power - of - a - power rule

We know that \(2^{3}=8\), and by the power - of - a - power rule \((a^{m})^{n}=a^{mn}\), \((x^{2})^{3}=x^{2\times3}=x^{6}\). So \((2x^{2}y)^{3}=8x^{6}y^{3}\).

Answer:

The equivalent expression is \(8x^{6}y^{3}\).