Write in exponent form: (2x^3 y)^3

Answer 1

To write \((2x^3 y)^3\) in exponent form, you can apply the power of a product rule, which states that \((ab)^m = a^m b^m\), and the power of a power rule, which states that \((a^m)^n = a^{mn}\).

Applying these rules:

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

Now, simplify each term:

1. \(2^3 = 8\)
2. \((x^3)^3 = x^{3 \cdot 3} = x^9\)
3. \(y^3 = y^3\)

Putting it all together, we get:

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

So, in exponent form, the expression is:

\[ 8x^9 y^3 \]