Question

Write in exponent form: (2x to the third power y)to the third power

Answer 1

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

Starting with \((2x^3y)^3\):

1. Apply the exponent to each factor inside the parentheses:
\[
(2^3)(x^{3 \cdot 3})(y^3)
\]

2. Calculate each exponent:
\[
2^3 = 8, \quad x^{3 \cdot 3} = x^9, \quad y^3 = y^3
\]

Putting it all together, we have:
\[
(2x^3y)^3 = 8x^9y^3
\]

Thus, the expression in exponent form is:
\[
8x^9y^3
\]