Question

use multiplication to expand the expression below. then compute and/or simplify.
$(-4xy)^3$
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 \((ab)^n = a^n b^n\). For \((-4xy)^3\), we can apply this rule to each factor inside the parentheses. So we have \((-4)^3 \cdot x^3 \cdot y^3\). In expanded form (showing the multiplication), this is \((-4) (-4) (-4) x x x y y y\) (or using the \(*\) symbol as required, it can also be written as \(-4 * -4 * -4 * x * x * x * y * y * y\) but following the sign rules, we know that multiplying three negative numbers will give a negative result, but first let's focus on the expanded form of the multiplication).

Step2: Expand the exponentiation

\((-4xy)^3\) means multiplying \(-4xy\) by itself three times. So \((-4xy) \times (-4xy) \times (-4xy)\). Using the multiplication symbol as \(*\) (since \(\times\) is inappropriate with \(x\) as a variable), the expanded form is \((-4) x y (-4) x y (-4) x y\) (we can also group the constants and the variables separately, but the key is to show the multiplication of the base three times).

Step3: Simplify the expanded form to the final answer

First, calculate the product of the constants: \((-4) \times (-4) \times (-4)= (-4)^3 = -64\). Then, for the variables, using the rule of exponents \(a^m \times a^n = a^{m + n}\), \(x \times x \times x = x^{3}\) and \(y \times y \times y = y^{3}\). So multiplying these together, we get \(-64x^3y^3\).

Expanded Form:

\((-4) x y (-4) x y (-4) x y\) (or an equivalent form with the multiplication symbols correctly placed, like \(-4*x*y*-4*x*y*-4*x*y\) but following the sign and variable rules, this shows the expansion of \((-4xy)^3\) as three multiplications of \(-4xy\) )

Answer:

\(-64x^3y^3\)