Question

In the following exercises, simplify each expression.

${\left(-10u^2{v}^4\right)}^3$

Short answer

The simplified form of the given expression is$\left(-1000\right)u^6{v}^{12}$

Step-by-step solution

Step 1. Given information.

The given expression is ${\left(-10u^2{v}^4\right)}^3$.

Step 2. Simplify the given expression.

Calculation of expression using product property,

$$\begin{gathered} {\left(-10u^2{v}^4\right)}^3={\left(-10\right)}^3·{\left(u^2\right)}^3·{\left(v^4\right)}^3 \\ =\left(-1000\right)·{\left(u^2\right)}^3·{\left(v^4\right)}^3 \end{gathered}$$

Now we use the power property,

$$\begin{gathered} \left(-1000\right).{\left(u^2\right)}^3.{\left(v^4\right)}^3=\left(-1000\right).u^{2.3}.v^{4.3} \\ =-1000u^6{v}^{12} \end{gathered}$$

Therefore, the simplified form of the given expression is$-1000u^6{v}^{12}$