Q. 154 - Intermediate Algebra

Question

Simplify ${\left(2p{q}^4\right)}^3{\left(5p^{6}q\right)}^2$

Step-by-Step Solution

Answer

Simplified expression is $200p^{15}{q}^{14}$

Step 1. Given information

${\left(2p{q}^4\right)}^3{\left(5p^{6}q\right)}^2$

Step 2

Here

$$\begin{gathered} {\left(2p{q}^4\right)}^3{\left(5p^{6}q\right)}^2={\left(2\right)}^3{\left(p\right)}^3{\left(q^4\right)}^3{\left(5\right)}^2{\left(p^6\right)}^2{\left(q\right)}^2 \\ =8\times p^3\times q^{4\times 3}\times 25\times p^{6\times 2}\times q^2 \\ =200\times p^3\times q^{12}\times p^{12}\times q^2 \\ =200\times p^{3+12}\times q^{12+2} \\ =200p^{15}{q}^{14} \end{gathered}$$