Q4. - Algebra 1

Question

Choose a term from the Key Vocabulary list above that best describes the given expression.

$\left(x{y}^3\right)\left(x^2{y}^4\right)=x^3{y}^7$

Step-by-Step Solution

Answer

The given expression can be best described as the power of a product.

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define the meaning of power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where, $a$ is any non-zero real number. 

Step 3. Write the best description for the expression x y 3 x 2 y 4 = x 3 y 7 .

Observe the expression, $\left(x{y}^3\right)\left(x^2{y}^4\right)=x^3{y}^7$.

Since, 

$$\begin{gathered} \left(x{y}^3\right)\left(x^2{y}^4\right)=\left(x\right)\left(y^3\right)\left(x^2\right)\left(y^4\right) \\ =\left(x\right)\left(x^2\right)\left(y^3\right)\left(y^4\right) \\ =\left(x^{1+2}\right)\left(y^{3+4}\right) \\ =x^3{y}^7 \end{gathered}$$

So, the expression, $\left(x{y}^3\right)\left(x^2{y}^4\right)=x^3{y}^7$ involves the products of the powers of $x$ and $y$.

So, it can be termed as the power of a product.

 

Therefore the given expression can be best described as the power of a product.