Write in exponent form: (2xsuperscript3y)superscript3

Question

(1 point)
Responses

2x9y3
2 x to the 9th power y cubed

6x6y3
6 x to the 6th power y cubed

8x9y3
8 x to the 9th power y cubed

2x6y3
2 x to the 6th power y cubed

Answer 1

To express \((2x^3y)^3\) in exponent form, we need to apply the power of a product rule, which states that \((ab)^n = a^n b^n\), as well as the power of a power rule, which states that \((a^m)^n = a^{mn}\).

1. Start with \((2x^3y)^3\).
2. Apply the power of a product rule:
   • \((2)^3\) gives \(8\),
   • \((x^3)^3\) gives \(x^{3 \cdot 3} = x^9\),
   • \((y)^3\) gives \(y^3\).

Putting it all together, we have:

\[ (2x^3y)^3 = 8x^9y^3 \]

Therefore, the answer is:

8x⁹y³