Question

use multiplication to expand the expression below. then compute and/or simplify.
$(3abc)^3$
answer attempt 1 out of 3
press the · button or type the * symbol on your keyboard to represent multiplication. using × for multiplication is inappropriate when x may be used as a variable. for the answer, type the base, then use the $a^b$ button or type the ^ symbol for an exponent.
expanded form:
answer:

Explanation:

Step1: Recall the power of a product rule

The power of a product rule states that \((xy)^n = x^n y^n\) for any real numbers \(x\), \(y\) and positive integer \(n\). Applying this to \((3abc)^3\), we can expand it as the product of each factor raised to the power of 3.
So, \((3abc)^3=3^3\times a^3\times b^3\times c^3\)

Step2: Calculate \(3^3\)

We know that \(3^3 = 3\times3\times3=27\)

Step3: Write the expanded form and the simplified form

The expanded form (using multiplication symbol as \(*\)) is \(3*3*3*a*a*a*b*b*b*c*c*c\) or using the power notation for each factor after expanding the power of 3 for the coefficient and variables, it can also be written as \(3^3*a^3*b^3*c^3\) (but the first form with repeated multiplication is more in line with "expanded" using multiplication).
The simplified form is obtained by calculating \(3^3 = 27\), so the simplified expression is \(27a^3b^3c^3\)

Expanded Form:

\(3*3*3*a*a*a*b*b*b*c*c*c\) (or \(3^3*a^3*b^3*c^3\))

Answer:

(Simplified):
\(27a^3b^3c^3\)