Sure! Let's break down the phrase "The cube of the product of 8 and a number" step by step into an algebraic expression.
1. Identify the unknown number: Here, "a number" is represented by the variable [tex]\( x \)[/tex].
2. Determine the product of 8 and [tex]\( x \)[/tex]: To express the product of 8 and [tex]\( x \)[/tex], we multiply them together, which gives us [tex]\( 8x \)[/tex].
3. Find the cube of this product: The cube of a number or expression means raising it to the power of 3. So, we need to cube [tex]\( 8x \)[/tex].
Putting these steps together, the algebraic expression for "The cube of the product of 8 and a number" is:
[tex]\[
(8x)^3
\][/tex]
To summarize:
1. Represent "a number" with [tex]\( x \)[/tex].
2. Multiply 8 and [tex]\( x \)[/tex] to get [tex]\( 8x \)[/tex].
3. Cube the result to get [tex]\( (8x)^3 \)[/tex].
And that's the final algebraic expression!
