Q2B. - Algebra 1

Question

Simplify the expression 

$\left(-4r{x}^2{t}^3\right)\left(-6r^5{x}^{2}t\right)$

Step-by-Step Solution

Answer

The simplified version of $\left(-4r{x}^2{t}^3\right)\left(-6r^5{x}^{2}t\right)$ is $24r^6{x}^4{t}^4$.

Step 1. State the multiplication rule of indices.

If the two terms have the same base (in this case x) and are to be multiplied together their indices are added.

 

In general: $x^m\times x^n=x^{m+n}$

Step 2. Collect the like terms.

In the expression $\left(-4r{x}^2{t}^3\right)\left(-6r^5{x}^{2}t\right)$, first collect the like terms. That is, write the constant terms together and the variables r,x and t together.

$\left(-4r{x}^2{t}^3\right)\left(-6r^5{x}^{2}t\right)=\left(-4\times -6\right)\left(r\times r^5\right)\left(x^2\times x^2\right)\left(t^3\times t\right)\dots \left(1\right)$

Step 3. Simplify the expression.

Now apply the multiplication rule in equation (1) and simplify further.

$$\begin{gathered} \left(-4r{x}^2{t}^3\right)\left(-6r^5{x}^{2}t\right)=\left(-4\times -6\right)\left(r\times r^5\right)\left(x^2\times x^2\right)\left(t^3\times t\right) \\ =24\left(r^{1+5}\right)\left(x^{2+2}\right)\left(t^{3+1}\right) \\ =24\left(r^6\right)\left(x^4\right)\left(t^4\right) \\ =24r^6{x}^4{t}^4 \end{gathered}$$