Q3. - Algebra 1

Question

Translate each sentence into an equation. 

The product of five and w is the same as w to the third power.

Step-by-Step Solution

Answer

The required equation is  $5w=w^3$.

Step 1. Apply the concept of multiplication of a constant and a variable.

A constant is a number like $1,2,10.5,$ etc. A variable is a letter or a literal used to signify an unknown quantity.

When a constant is multiplied by a variable we just append the constant in front of the variable.

We are given a constant $5$ and a variable $w$, so their product will be $5w$

Step 2. Apply the concept of raising variable to an index.

When a variable is multiplied by itself we raise the index/exponent of the variable by two, when it is multiplied once more to this product we raise the index to three. In this fashion, variables are written for example,

 

$\begin{array}{l}x\times x=x^2\\ x\times x\times x=x^3\end{array}$ 

Thus $w$ raised to the third power is written as

 $w^3$

Step 3. Evaluate the two results.

To get the final expression we equate the results of steps 1 and 2 to get:

 

$5w=w^3$ 

Thus, the required equation is  $5w=w^3$.