Question

$\mathbf{\left(}{\mathbf{q}}^{\mathbf{2}}\mathbf{\right)}\mathbf{\left(}\mathbf{2}{\mathbf{q}}^{\mathbf{4}}\mathbf{\right)}$

Short answer

The simplified version of $\left(q^2\right)\left(2q^4\right)$is $2q^6$.

Step-by-step solution

Step 1. State the multiplication rule of Law of indices.

If the two terms having the same base are multiplied together, then their indices are added.

In general:$x^m\times x^n=x^{m+n}$

Step 2. Simplify the expression.

Apply the multiplication rule to simplify the given expression.

$\begin{array}{c}\left(q^2\right)\left(2q^4\right)=2\left(q^2\right)\left(q^4\right)\\ =2\left(q^{2+4}\right)\\ =2q^6\end{array}$

Step 3. State the conclusion.

As there are no other variables, just add the powers of variable q and the expression is simplified.

$\left(q{}^2)\right(2q^4)=2q^6$