Q. 151 - Intermediate Algebra

Question

Simplify ${\left(\frac{1}{2}{x}^2{y}^3\right)}^4{\left(4x^5{y}^3\right)}^2$

Step-by-Step Solution

Answer

Simplified expression is $x^{18}{y}^{18}$

Step 1. Given information

${\left(\frac{1}{2}{x}^2{y}^3\right)}^4{\left(4x^5{y}^3\right)}^2$

Step 2

Here

$$\begin{gathered} {\left(\frac{1}{2}{x}^2{y}^3\right)}^4{\left(4x^5{y}^3\right)}^2={\left(\frac{1}{2}\right)}^4{\left(x^2\right)}^4{\left(y^3\right)}^4{\left(4\right)}^2{\left(x^5\right)}^2{\left(y^3\right)}^2 \\ =\frac{1}{2^4}\times x^{2\times 4}\times y^{3\times 4}\times 16\times x^{5\times 2}\times y^{3\times 2} \\ =\frac{1}{16}\times x^8\times y^{12}\times 16\times x^{10}\times y^6 \\ =x^{8+10}\times y^{12+6} \\ =x^{18}{y}^{18} \end{gathered}$$