Question

use multiplication to expand the expression below. then compute and/or simplify.
$(4b)^3$
answer attempt 1 out of 2
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 exponent definition

An exponent \( n \) on a product \( (xy)^n \) means multiplying the base \( xy \) by itself \( n \) times. For \( (4b)^3 \), \( n = 3 \), so we expand it as \( 4b \times 4b \times 4b \). Using the allowed multiplication symbol (\(*\) or \(\cdot\)), the expanded form is \( 4b * 4b * 4b \).

Step2: Simplify the expanded form

Calculate the product of the coefficients and the variables separately. The coefficient part: \( 4\times4\times4 = 64 \). The variable part: \( b\times b\times b = b^3 \) (by the rule of exponents \( x^m\times x^n = x^{m + n} \), here \( m = n = 1 \), so \( 1+1+1 = 3 \)). So the simplified form is \( 64b^3 \).

Answer:

Expanded Form: \( 4b * 4b * 4b \)