Question

Simplify the expression

$\left(5u^{4}v\right)\left(7u^4{v}^3\right)$

Short answer

The simplified version of$\left(5u^{4}v\right)\left(7u^4{v}^3\right)$ is $35u^8{v}^4$.

Step-by-step solution

Step 1. State the multiplication rule of Law 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,$\left(5u^{4}v\right)\left(7u^4{v}^3\right)$ first collect the like terms. That is, multiply the constant terms together and the same variables together.

$\left(5u^{4}v\right)\left(7u^4{v}^3\right)=\left(5\times 7\right)\left(u^4\times u^4\right)\left(v\times v^3\right)\dots \left(1\right)$

Step 3. Simplify the expression.

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

$$\begin{gathered} \left(5u^{4}v\right)\left(7u^4{v}^3\right)=\left(5\times 7\right)\left(u^4\times u^4\right)\left(v\times v^3\right) \\ =\left(35\right)\left(u^{4+4}\right)\left(v^{1+3}\right) \\ =35\left(u^8\right)\left(v^4\right) \\ =35u^8{v}^4 \end{gathered}$$